 Hello everyone, the course of business forecasting. Today we will enter into the module of ARIMA, but before we go in details of ARIMA, we will understand the basic concept of SEF and PSEF. These two terms are very important to understand the steps of ARIMA. In ARIMA, we have auto regressive model, we have moving average process and then we have ARIMA model and auto regressive integrated moving average process that is called ARIMA model. All these three four models we will learn in detail, but before that we need to understand the concept of autocorrelation function and partial autocorrelation function. In time series models, you have the same variables data right with time. So therefore when you develop a auto regressive model, you need the correlation between the data of current lag and the past lag and their features. In order to understand that lags and the correlation between the current data and the old data, how they are interdependent among each others, you need SEF and partial autocorrelation function. So you need to study that today and then we will enter in the next day into the ARIMA model. Now even before we go to SEF and PSEF, let us understand or require the basic concept of correlation coefficient and partial correlation. If you know these two concepts effectively for basic regression analysis between any two variables, that concept can be extended to time series data and we can understand easily the SEF and PSEF functions. So first what is correlation coefficient? We all know correlation coefficient is the correlation, linear correlation between or linear relationship between two variables. If you have a variable say x and y, x and y and if you have a data set, you can find the correlation coefficient between them using excel right. So this is the formula covariance by variance of x and variance of y. And then using that formula, you can calculate the correlation coefficient of the two variable x and y. This is the linear relationship between the or how they are correlated that can be calculated. The range of correlation coefficient generally lie between minus one and one. Now the question is that if there are say three variables and you need to find the correlation between x1 and x2 and x3 is involved over there also which has an impact on x1 and x2. In that case, look at the definition the correlation between two variables may be sometimes be affected by a third variable or other variables. In that case, you need to eliminate the impact of the other variable to find the correlation between the main two variables. That means if you have three variables say x1, x2 and x3. Suppose three variables you have and you need to find the correlation between x1 and x2 or xyz whatever but x3 will have an impact between x1 and x2 on. In that case, the impact of x3 has to be eliminated. Then only the correlation of x1 and x2 can be calculated otherwise there will be a interdependency among the variables. Now that correlation is not the actual correlation. So therefore we need to calculate the partial correlation. So let us see what is partial correlation. Here I have mentioned few more examples to get a clear picture of the idea of what is partial correlation. Correlation coefficient is simple the relationship between the two variables. But in partial correlation what happens you know the third variables or the other variables might have an impact. So you have to eliminate that. Look at the example the correlation between prior experience suppose you are a candidate for job or whatever prior experience and job performance may be affected by the educational qualification. Imagine if educational qualification is another variable which might have an impact on your prior experience as well as the experience for in your profile in your CV as well as say you know job performance. Similarly you can think about that you know the written test and interview might have an impact from prior academic performance. So your academic performance will have an impact on your written test and interview. In that case if you want to find the correlation correlation between written test and interview your prior academic data performance is having an impact on that. So therefore you remove the impact of prior academic performance and then find the correlation between written test and interview completely you know as an independent variable no impact of academic performance. In that case if you find this correlation between the written test and interview after removing the impact of performance academic performance as another variable say then this correlation coefficient between written test and interview will be called as a partial correlation coefficient. This into understand and in time series we required this part this partial correlation coefficient rather than correlation coefficient both are required but these two are major concept in understanding SCF and PSF I will come to that now and then the ARIMA models. This is the basic recap of correlation and the partial correlation right now how to calculate the partial correlation the concept of correlation coefficient is easy and you can calculate it in basic Excel but for partial correlation you need some steps because the concept that example that I have given you can understand but how to execute it in Excel say or in data that I have mentioned here the steps look at the steps here how to calculate the partial correlation between the data. Suppose you have three variables as I mentioned X1 capital X1 say X2 and X3 three variables and you want to remove the eliminate the impact of X3 among X1, X2 say. So now what we have done first you take the center of the data like you take the calculate the average of each data average of each data and then like you have a data say you have the data say you take the average of these data this is a bar average of the data same way for all three variables all three parameters you know in Excel you might have you can understand that calculate the average of all of them and then take the differences you will get the center of all of them take that data okay after differencing from the mean and then let us note them with new variables say small x1 x2 x3 these are the new representative now because we have not taken that we have scaled down the data now the variation has come down only the gap or variation we are calculating now we are counting now so these variations of the data will consider of each variables now this will be replaced with small x1 small x2 small x3 now say because we have taken the differences only the differences among them from their mean this data will take forward to calculate the partial correlation among the actual variable X1 X2 and X3 now we have to remove the impact of X3 from X1 and X2 right so you regress next step you regress X1 upon X3 and X2 upon or against X3 so now first you regress X1 against X3 so we have done that remember here you do not need since we have already done the centered of the data you do not need the intercept part right only the slope part is sufficient so you do not need the intercept part force the intercept equals to 0 in your excel and then you do the regression you will find the you know direct slope which will pass through origin not a matter so you found the relationship between the X3 and X1 how X3 is explaining on X1 or how X1 is explained the new variable the scale variables after taking the center of the data how the X1 which is represented of capital X on main variable your objective is to calculate the correlation or partial correlation between capital X1 and capital X2 but X3 is coming into the picture which is impacting X1 and X2 so you have to remove eliminate the impact of that that you are going to do now so now what you do you regress the new scale data X1 center data X1 with X3 that means how X1 is explained by X3 right the variations this we have developed similarly we calculate regress X2 against X3 that means how X2 small x2 is explained by X3 that you can calculate take the difference of them you will find a new component say U1 and U2 I have noted here so these are the new component the differences between the scale data of X1 and its regress data with X3 so this values you will get suppose this is component one between X1 and X3 of regress data and this is say X2 and X3 so these two data if you collect and if you calculate the correlation coefficient whatever this will be called as a partial correlation coefficient actual correlation coefficient partial means actual without having any impact of X3 so that we have removed now and this is nothing but the partial correlation of two variable where the third variable impact has been removed look at here therefore the correlation between U1 and U2 represent the partial correlation clear now I will explain that using excel later so these are the two basic concept correlation coefficient here which we have discussed in this slide and partial correlation which we have explained the steps here the calculation process the concept is mentioned here but the steps of calculation is mentioned here so these two will help you in calculating SCF and PSF now which will go to Arrimer model now look at this formulas here you can see no term this particular formula in many books this will be mentioned here using this formula you can calculate in excel you can calculate the PSA what is that the partial correlation between 1 and 2 X1 and X2 given X3 equals to nothing but the correlation coefficient between 1 and 2 minus 1 and 3 into 2 and 3 and this this so this formula Arrimer popular formula you can use this formula to calculate the partial correlation so these steps you can get otherwise you can follow these particular steps that I have mentioned or direct this formula anyone you can follow we will follow these particular steps that we have discussed today now look at the auto correlation now we are going to go to the time series data now we have entered into the time series data right now in time series data we have same data say y right so y1 y2 only one variable you do not have any you know independent variable here like this you do not have any independent variable and you need to find the correlation among the data what does it mean it means that you want to see how your current data are being impacted by the past data that means how say you are at this position say how your y6 is impacting by y5 how your y5 is been impacted by y4 or how y4 is explaining y5 that you want to calculate that we call it is a lag past like 1 lag 2 lag 3 lag like that this way how like this is stock price or say you know temperature how yesterday's temperature has a impact or how much impact it has in today's temperature so that correlation that linear relations we want to find this relationship we call it is a auto correlation why auto auto correlation coefficient because this correlation coefficient are not from 2 independent variable 2 different variable not it is not like that x and y and you are finding correlation coefficient between them here effectively you are having the same data sets and among them you are trying to find the correlation therefore we call it is a auto correlation more detail I will explain this is the formula you can see covariance between current data and say k pure lag right and that correlation you want to find say y4 so y6 and y5 or y6 and y4 y6 and y3 so the impact of the older lags or older data you can also calculate through correlation coefficient we will understand the first case like only one period lag and then you can extend that concept to the older like like multi period lag also so this is same logic covariance of current and the older data that current corresponding period you want to consider so suppose this is y6 and this is suppose y3 so you want to calculate the covariance correlation coefficient auto correlation among them so you calculate the covariance and the variance among them also and this will come as a to some extent say you know square because it is the same data so ultimately it will be the same almost and then you can calculate using this formula right so now we will find the plot as well as the lag impact on them right so here let us take one practical example and we will plot the SCF as well as the concept calculations we will illustrate here now suppose we have taken 3 months data of TCS from NSC nesla stock exchange we have taken the TCS data actual data we have taken and we will understand the SCF the basic correlation coefficient you know right basic correlation coefficient you know which I have shown you in the previous slide and the basic calculation formula you can calculate between two variables first let us understand the SCF and then we will go to the TACF now remember here it is a time series data it is a time series data you do not have any you know kind of two variable three variable same variable here and the other say stock price of TCS how will calculate the SCF what is the concept let me repeat it again suppose here you have the data say y this actual data suppose here y 1, y 2, y 3, y 4, y 5, y 6, y 7, y 8 dot dot dot then what you do in excel you take a new variable say suppose this is y t this is y t minus 1 just copy this data and paste one row below in your excel y 1, y 2, y 3, y 4, y 5, y 6, y 7, y 8 like this remember this data we have copied this data we have copied and pasted one row below now you delete the first row and delete the last row say delete the last row now you have a pair of data look at this pair of data let me put a highlight you will get a letter clarity look at you have this data and you have these data sets right we have the pair of data now same pair of data and if you ask the computer or your excel that find a relationship between this data set and this data sets so excel will consider this as one variable say and this is another variable say so this suppose excel will consider let me open the pane again so excel will consider this say you know one variable say say x 1 and say this is to say say x 2 or you can say excel will consider this as a y t and this is y t minus 1 so that means say you know or say as I mentioned x 1 and x 2 say so it is a yesterday data say this is nothing but yesterday data because you have taken the t c s stock price so here this yesterday this this y 1 has come here you can think then y 2 has come here y 3 has come here y 4 has come here it means that y 5 now you have taken a pair right you have not taken a pair so y 5 will be dependent on y 4 this is your say y this is your x or x and y whatever your x 1 x 2 you can consider so now you have a pair of data say just all yes these are all yesterday these are all yesterday actually right as compared to this first column and these are all today these are all today so wherever you are you are today you appear at y 7 y 7 here today stock price y 6 y 0 yesterday stock price but why y 6 you have kept in your excel in the same row of y 7 so this pair of data if you give it to excel and if you ask excel to calculate the correlation coefficient excel will calculate the correlation coefficient suppose 0.8 but this correlation coefficient are not simple correlation coefficient this is auto correlation coefficient why because this is the auto data same data done we understood the correlation auto correlation coefficient or auto correlation function now we have to plot it right so what do you do you take the data and copy in the next column but one row below then drop delete the first row and the last I will show you in excel and last row then you have a pair of same data sets you ask the excel to calculate the correlation coefficient simple correlation coefficient formula that I have shown in the previous ppt you can slide you can calculate so this is nothing but correlation it is but actually auto correlation coefficient right so now you draw that so here your a cf auto correlation function and this is your say lag right time say or you can say lag so now with the same data if you draw the same your correlation coefficient will be always one right if you copy the same data y1 y1 y2 y2 it will be always one so we are not interested about that we what would like to study from the first leg first period so leg one you consider leg one so this this correlation now yt and yt minus one or today and yesterday you suppose you found 0.8 suppose you found 0.8 you draw it 0.8 now you calculate you might say the rates are of my stock price might depend on debut for yesterday also so today's back also so why you are not considering that correlation among them it might have an impact of today's stock price also so you copy their data again and then paste from here so y1 y2 y3 y4 y5 y6 like this this and then you drop the first two row just delete the first two row and the last two row you will have a pair of data now here you can see y1 has come here sorry it will start from here y1 y2 y3 y4 y5 like this so you can see look at this data set now look at this let me put a different color highlight with green so look at this this data set now even here you can you can see this so here effectively your y3 will depend on yesterday y2 and y1 so current stock price will depend on yesterday's stock price and debut for yesterday stock price now you want to find the correlation among them this correlation are called the autocorrelation also so now this will give you the SCF like you know AR model auto regressive model of order 1 or order 2 I will discuss in the next class but now let us focus about simple SCF and PSA so here you can see this relationship between current and debut for yesterday one day back if you find the correlation you might find it here same maybe say 0.6 so it is 2 days like and then again if you put one more data you may find a lack correlation between them say you know 0.7 say 0.5 so these are nothing but the SCF plot or correlogram one part of correlogram that is called SCF plot PSA we will discuss later now so this is what the SCF and plot here I have shown you the calculation process here you can see we have the actual data then copy them and paste one row below one row below one row below one row below and now suppose you want to calculate the SCF of order 1 SCF of order 1 that means you just take current and the 1 lakh below yesterday and you calculate the drop first delete first row and the last row you will get a pair of data you calculate your first correlation coefficient auto correlation coefficient because at the same time series data therefore we have to use the word auto auto correlation coefficient same formula simple we are using the word auto because you are same data you are copying and you are considering as a dummy independent variable and therefore we call it a SCF of lag 1 then if you calculate current and the 1 lakh older so it will be a 2 days back data so in that case the correlation between them will be called SCF of lag 2 and you can calculate here look at here you can take that data and directly all the data you can take and you can if you have a larger amount of data directly you can calculate your SCF graph function through this formula of correlation and you found the lag and the corresponding correlation you can see so here you know with the immediate data you have a maximum impact the correlation is very strong the next day correlation is little lower then it is reducing actually the other means older data of TCS are not impacting to the current data much but there is a relationship there is a relationship this is called the SCF plot drawing in correlogram clear everybody I believe now let us go to the next level that is called PACF calculation same logic just you need to understand the partial auto correlation not the actual correlation because the auto part are being there with the same data but the point here is that here in this case in this case you have calculated the direct correlation right so here you can see how much in the first case it is 95% the correlation the yesterday stock price is impacting to the stock price with almost 95% that it is explaining look at the day if you rest it is also 90% 90% but the practical case is that this is the direct correlation but the practical case since it is auto data the second day data like day before yesterday data will not have this much of impact 90% impact with your current stock price the reason is that there is an intermediate data called yesterday which was in between so when you take the data of yesterday in your current data and calculate the correlation this is fine but when you go one luck back or one day back day before yesterday in that case your the impact of day before yesterday data in the current data should not be the same you have to take the partial impact of that because yesterday some day was a today then day before yesterday was a yesterday and then yesterday was a today so that impact also is there already so you cannot take direct value of day before yesterday into your current you have to see the remove the impact of yesterday between the current calculation correlation between today and day before yesterday this is called the partial correlation let's see how we can calculate it this is the formula same formula PSA with the same luck now now we are not taking the x1 x2 etc we are taking the same auto data so you can take YT the not a general formula people use like this YT with how many luck like 1 lakh 2 lakh 3 lakh if you take 1 lakh then YT and YT minus 1 if you take 2 lakh then YT and YT minus 2 so the relationship is said to be direct and exclude the relationship with the intermediate lag intermediate lag has to be removed suppose that for example if you want to calculate the impact of say today and yesterday today and yesterday is fine but today and day before yesterday it may not be like this it may be very less amount the reason is that it is a partial impact you cannot take the full input the intermediate lags impact has to be removed right so that we are going to do through PSA now what are the first steps I have already mentioned that simple partial correlation calculation steps same calculations we will be using here but in that case we have talked about x1 x2 and x3 and we have seen the impact of x3 on x1 and xx1 and x2 that we are not going to do here what we will do we will consider here now YT current I would say YT and then YT minus 1 day before yesterday and day before yesterday right we want to see the calculation the PSA between these two YT and YT minus 2 these you want to see YT and YT minus 2 we want to see this rather I will write the arrow here this side so the impact of this YT minus 2 on YT the correlation we want to calculate but this correlation should be called as a partial correlation or partial auto correlation because it's auto data same data same time series data you have put in a different column only but it's the same data but Excel will understand these as a independent some variables but we know it is auto data so therefore we need to find these two are same same simple partial will be the same as it is auto correlation because it's just yesterday direct impact you have to take but for debut yesterday you cannot take the direct full impact you have to take partial impact because because intermediate yesterday is already been involved over there so you cannot take the direct impact because it will be very less impact because you are taking full impact of yesterday so only partial impact of debut yesterday you have to consider how to calculate it same logic here what you have to do in this case here you have to remove the impact of YT minus 1 from YT and YT minus 2 and then center the data and calculate the actual partial correlation between YT and YT minus 2 so here steps are center the data of all these three data you might have some you might say so these are the same data only one row below etc so how to calculate centers and everybody will have the same center average data everybody will have the same average because one data if you delete it will not have much impact if you have a longer amount of data so everybody will have the same average and then you calculate the center center value will be different so these data this the scale data will consider and then we'll calculate the partial correlation so here first to the center data then calculate the slope of YT and YT because we want to calculate the PSCA between YT and YT minus 2 debut yesterday capital Y say we want to calculate that that is our objective the partial between partial autocorrelation function or partial autocorrelation value between YT and YT minus 2 we want to calculate that right debut yesterday impact on current the partial impact of that actual impact of that in today's stock price so that you want to calculate so center the data first for every three all three today yesterday and debut yesterday then calculate the slope like the regress you have to calculate the slope and regress and slope of YT against YT minus 1 slope of YT minus 2 against YT minus 1 because here we want to remove the impact of yesterday from both from YT as per the formula PSCA from YT and YT minus 2 and then once we'll get the you know impact less data between YT and YT minus 2 and then calculate your correlation that will be a partial correlation then calculate the component of YT and you know YT minus 2 component you can say error not error but it's a gap differences right and then calculate the correlation between them this correlation are nothing but the partial correlation let's see and how we can draw you'll see the actual impact it will be very less actually not the actual partial the actual correlation here you can see the actual correlation 90% 85% but it will first time will be the as it is but after that you will see the partial will be very less maybe these these these it will be fall down quickly because older data will not have a much impact because it is a partial impact we are considering let's see how it works now the steps center the data then regress after taking the same center data regress the scale data or the impact of current we have taken a notation of YT minus white small YT in the previous PA partial correlation slight I have shown that so same notation we'll consider so YT the impact of YT minus 1 yesterday scale data yesterday on YT and impact of YT minus 1 on YT minus 2 here we are calculating the correlation between the partial correlation between these two so we will consider these two variables and we will remove the impact of YT minus 1 remember this differences this concept here now if you regress now this we are considering as independent variable now after scaling scaling down the data so this impact we want to calculate right and you want to remove so what do you do regression and calculate the slope and the corresponding regress regression data regress data and then you will find the difference between them as your new component the gap similarly YT minus 1 on YT minus 2 and you will get the component so these two component you will get ET and ET minus 2 calculate their correlation simple correlation that will be a partial correlation so now you take these two and calculate your partial you can either use this formula or that formula or the steps that I have mentioned let's see so here you take the actual data then one day back look at YT minus 1 and 2 days back just copy and paste and you can get to know like this I have removed all this I'll show you in Excel and then take the average of this data average of this data average of this data now you are in Excel now Excel have three variables this variable this variable this variable and you want to calculate the PSN now Excel will not understand the same data but you know it is auto data so they everywhere will use the auto part auto work otherwise it is just simple partial correlation we are calculating the steps that I have mentioned earlier so now we calculate the center of each of them average of all of them all this data to some extent average value will be the same and then you calculate the center so this minus this this minus this this minus this for IT current data now you calculate the center this minus the average data will get the center of second data second you have the yesterday data t minus 1 data and center of depth if you yesterday data that is t minus 2 data so this is the scaled down data so this is we are using small yt small yt minus 1 note as a notation small yt minus 2 right so these notations we are considering now the capital yt yt minus 1 and yt minus 2 for the time being we are not considering scaled down data we have taken now we call it is center data take the center data calculate the slope between these two slope between these and then once you get the slope you calculate your integration value and that will give you the component the ET and ET minus 2 these two components the current like you know partial data will give you the partial correlation or the difference data will give you the new partial correlation or PSEM value so now what you do you can think about say you know center data you have already calculated now calculate the slope between these and this look at here similarly calculate the slope between these and this look at here you have calculated the two slope note down once you get the slope you can get the regress line y equals to mx y equals to because intercept we have considered 0 so that and this the additional parts say the component but none to add the difference this minus this you will get the component here we have done that look at two slope we found corresponding regression line you will get here we have calculate the regression line you can see and if you subtract that from your actual data now center data is your actual data right to some extent though it is a scaled data we are considering actual data so you take the difference sorry you take the difference among them you will get the component new component now you have a new data fresh data after subtracting the you know impact of the intermediate data and then calculate the correlation between these two data set this will be nothing but or we consider auto auto partial correlation coefficient clear here you can see you can calculate this this data sets are nothing but this and you calculate your correlation between them this is nothing but effectively found the partial correlation between capital yt and yt minus 2 so yesterday today and day before yesterday not yesterday this correlation found this is called partial correlation earlier it was 90 percent now you found only minus 10 10 percent imagine that you can see here earlier it was how much here you can see 90 percent look at 90 percent there if you restart the impact on current data but now you can see even here also 86 83 you can remember it will fall down suddenly because partial impact you are considering this huge impact will not be there so therefore you cannot take in Arima models I will discuss in the next class you cannot take a shape graph and corresponding impact you have to take the PSA graph in calculating your lag in developing your regression model auto regressive model in Arima I will discuss that detail so here you can see it was currently 9 ACF value is 90 percent auto correlation but partial autocorrelation was minus 0.1 you can see here it is minus 0.1 here you can see the further graph minus 0.1 and then you can see 0.3 only 0.03 3 percent only here it was 86 percent earlier here it was 90 percent here it was 90 percent you can see so it is drastically falling down look at here so this is what the first one immediate data will have a almost same data line 95 percent whatever then onwards you will see the impact of it this is what the partial autocorrelation coefficient or partial autocorrelation function and this is called the correlogram of PSA graph the previous one the correlogram of SCF put together we call it is a correlogram of time series data now this part we understand in excel and then we will wind up today's session let's go to excel so here we have taken the TCS data of last three months say three months so October to October 2023 to December 2023 three month data we have taken so here the data we have taken from the NSE site and you calculate the SCF first you can understand the SCF look at the tag here in the sheet SCF calculation simple you copy the data and paste one row below like copy and paste one row below here I do not have to copy because my data will change calculation will change but you can do that here right so you can see 2 lakh 3 lakh just you have copied and paste now you want to calculate the SCF between current data YT and YT-1 simple calculate the correlation coefficient you will find 99% this one will find this one as the correlation between current and yesterday right or one day lack data one day period old period data so it's a TCS data for stock price you can consider as I said Dow Jones or Nasdaq data also you can consider you can also consider say you know gold price you can also use the temperature or say crude oil wherever you want to apply the Arima model these concepts will help you in developing the Arima model today we are discussing the background SCF and PSF concept once you understand this Arima model will be very easy to understand just you know maybe 10 minutes will be taken to understand the AR process and then MA process then ARMA process one by one we will discuss in the next one one or two session so now if you want to calculate the lack between current and yesterday one lakh one or lack of time series data to take this data and this data calculate the correlation coefficient now you want to calculate 2 lakh 2 period land data so consider this data and 2 days back data like I mean the lack 2 of day before yesterday data you consider and you calculate your correlation coefficient like in that case you take data from here and so here so what you do correlation between say these data let me say today and then we will consider say so we take from here till this last data we will delete calculate so you have calculated the correlation between yesterday today and day before yesterday here I believe it is clear to everybody now look at this this and this so this is nothing but the correlation between current data and day before yesterday so this is what your SCF calculation similarly here I have drawn the graph correlogram graph here you can see 0.95 then 90% then 86% all this data we have plotted here they are SCF calculation now you go to PSEF five steps first step is that center the data first you calculate the average so we have taken the average of the data so what we have done we have suppose only three period we have taken today yesterday and day before yesterday more detail you can develop in different software say you know Ithon etc but the basic steps of PSA calculation I have shown here so now this is your current data this is your yesterday data this is your day before yesterday right so now you have to take the center of the data the scale data you have to take so first you calculate the average of all of them everybody will have the same average as I mentioned in the PPT take the center of the data current minus average for everybody current minus average for everybody current minus average now this data look at this column number f and g this data is your center data right now what you do you calculate the slope between current and you want to see we see the partial correlation between yt and yt-2 right and you want to remove the impact of yt-1 so this day before yesterday how it is impacting to your today's data that you want to calculate right so therefore what you do we calculate the equation between current and yesterday with scale data center data and between day before yesterday and yesterday yesterday will be your with scale data will be your independent variable here to calculate the regression so now here you can calculate the you can calculate the you know slope between current and yesterday with center data and slope between day before yesterday and yesterday look at day before yesterday and look at h is first and then g is coming second. So calculate the correlation or slope between them also. Now using these slopes you can calculate your components. What is that? The current minus the regress data. Current minus regress data so you know slope into this value minus actual minus the current minus slope into this value. So you can calculate using this formula you can use this formula look at my mouse and you can calculate the center new component data for everybody look at here. So you are taking first h and then you are subtracting the slope into yt minus 1 look at slope into yt minus 1. You are subtracting that from yt minus 2. So yt minus 2 is your main data variable data and yt minus 1 is your independent data for the sake of understanding. So you are seeing the impact of that. So now you found these two components k column k and column l after eliminating the impact of yesterday. Now these are fresh data. Like you know the impact or the dependency of yesterday is removed from both from today's data and day before yesterday's data. Now you have the fresh data today and day before yesterday. Find the correlation among them. Simple correlation among them. This correlation is nothing but the partial correlation between actual stock price of today and day before yesterday. Between the actual temperature of today and day before yesterday. Between the actual kudal price of today and day before yesterday. This partial correlation coefficient you have to consider in your algorithm model. How? Why? That we will discuss in the next class. We can see the PSA here. So this if you come back to your PPT you can see this I have mentioned here. Here you can see this 0.1 minus 0.1 and 0.03 are coming here into your PSA calculation. Not the actual correlation it is a partial correlation. But in PSA because 90% 86% but here it is just 0.1 0.3 kind of thing. So imagine this is what the PSA. This we need to carry forward to the algorithm In the next class we will discuss the introduction of auto regressive model and the moving average process and how the SCF and PSA concept are being used there to evaluate to calculate the AR model and MA model or ARMA model that we will discuss in detail. Thank you.