 Hello and welcome to the session. In this session, we discuss some of the concepts related to moving average. First of all, let us look at the introduction of time series. Now, most of the business and economic data like prices, national income, population, imports, exports, production, consumption, sales, brackets, burn exchange reserves, etc. are collected on the basis of time such as days, months, years. Now, these data are subject to regular and irregular changes constantly and these data help the government to estimate the likely population in the next 5 to 10 years so that disaster planning may be done in advance to fulfill the needs of the increased population like food, housing, electricity, fuel, etc. Such data are called time series or we can say the statistical data collected at the successive intervals of time of a period such as the commodity period taken at the intervals of time. This is with the help of an example, a couple of time series that includes the production of coal in terms from the year 1905 to 1910. Thus we can say that the time series is a binary distribution, one of the two variables being time and the other the value of the phenomena measured at different intervals of time and when the values of the value rates are plotted at this time on a graph paper then the points obtained are joined by three line segments and you obtain a graphical record of the behavior of the value rate and this is called the graph of a time series. Now we have got all these points on the graph, so we have plotted all these points on the graph and here this point shows that in the year 1905 we have plotted the other points also, now by joining all these points by straight line segments a graph of the time series is obtained and which is called the historical graph of the time series and it gives a rough idea about the nature of changes in the values of the value rate with the time and this historical graph shows that on the whole the production is increasing and now let us discuss variations or fluctuations. Now here the graph of the time series shows the production of coal in terms in the particular years and here you can see that in the graph of the time series there are ups and downs over the short durations variations in the values of the value rates are called that is the variation in the values of the value rate used by the historical graph shows fluctuations and fluctuations are also called variations of oscillations Now let us discuss the four types of fluctuations the secular long term trend Now the secular or long term trend refers to a genuine pregnancy that sees data increase, decrease, stagnate, a long period of time say that any time series shows various fluctuations from time to time but in long periods the tendency to grow or decline persists that is it has the increasing or decreasing trend in one direction and this is called a secular trend or long term trend for example in India population the consumer goods agriculture production etc has a tendency to increase with time period of a rupee except decrease with time seasonal variations Now the seasonal variations are the periodic variations in time series which occur regularly in definite and are up to be anticipated Now these variations occur due to weather, visual forces the price of food rates are low at the time of harvesting when foods rise in price become cheap during summers and during festivals and land seasons demand for certain commodities increases technical variations Now the secular variations are the acidity variations and we can also describe it as repeated growths at sums over regular periods of time experienced by many industrial or financial sectors these periods are short but larger than a year still it do not affect the trend changes it on a graph then we find that this show movements from these to class and back at regular intervals of time and the periodic moment is in the form of cycles but each cycle and its longer phase is different random fluctuations Now these are the short term variations in time series which occur due to certain accidental causes industrial strikes etc Now these variations does not occur in a systematic way hence their measurements and anticipations are difficult moving on which in this method variations due to certain changes for a specified number of successive years and the time interval covering the number of years is called the period of cycles This is it with the help of an example Now consider the following data Now in this data the number of short vacancies in the months for the particular years that is in the month of March in the year 1996 the number of short vacancies were 122 and similarly for the other months it is also given Now this is the time series of a graph for the given time series that is the months in the particular years So we have captured all these points of the graph that is we have captured the graph for the time series Now here you can see that it is difficult from this graph to see where the number of short vacancies has risen and fallen over the three years of this variation within each year which was this variation by working on a moving average of the consecutive pieces of data Now here we are having groups of four The first moving average is the mean of the first four values Now let us denote it by M1 So M1 is the mean of the first four values and calculating with a 16 by 4 which is equal to 179 Now the next moving average M2 is found by moving up one place of the values from June 1997 that is we will leave this value and we will add the next four values we will obtain M2 equal to 176 the value for the month of December in the year 1998 has taken into account therefore we are finding a four point moving average and we can name the table for the four point moving average which in which we will place the four point moving average is for which it was generated that is M1 is generated by the values in the months of March, June, September, 1996 so we will place M1 in between the months of June and September in which by the values in the months of June, September, December in the year 1996 and March in the year 1997 so we will place M2 in between the months of September and December in the year 1996 now we have calculated the four point moving averages for the given data that is we have calculated M1, M2, M3 and so on up to M9 but the four point moving averages on the same graph as our original data and each average is plotted at the midpoint of the values from which it was generated so we have plotted all the moving averages on the graph and on general average points we are getting a much smoother graph of the moving average in this case shows a slight downward trend and this means the number of jobs they can see is fairly between the beginning of the year 1990 of the year 1998 the fluctuation due to the cyclical changes are eliminated after being made for a specified number of successive years and as the graph has such a smoother graph than that of the original graph of the time series therefore the moving average gives a clear invitation of the trend of the set of data I have learnt about related to moving average and this completes our session hope you all have enjoyed the session