We will be doing box Jenkins technology in this video or PJs technology. So let's talk about what is box Jenkins technology. The box Jenkins model is a mathematical model designed to focus data from a specified time series. The box Jenkins model can analyze many different types of time series data for forecasting its methodology uses differences between data points to determine outcomes. Overall, the methodology allows the model to pick out trends using autoregression moving averages and seasonal differencing. In order to generate forecasts box incomes analysis refers to a systematic method of identifying fitting checking in using integrated autoregressive moving average Arima time series models if future values can be described by the probability distribution the series is said to be statistical or stochastic process.

So, the objective of auction kins is trying to find an estimate a statistical model which can be interpreted as having generated the sample data. If this estimated model is then to be used for forecasting, we must assume that the features of this model are constant through time and particularly over future time periods that we must have either stationary time series or a time series that is stationary after one or more differences. So, for applying the DDS technology that is we are doing animal modeling using the BJs technology or using the Jenkins technology there are also the condition is that your data has to be stationary and if you do not have a stationary data, we have to convert the data into stationarity by doing the differencing technique Now, let's move on to the steps that we have to adapt for blockchain in StatCrunch. The most important question while modeling a time series is how does one know whether it follows a purely a process that is what is the value of p Pease optimal lag for AR model or a purely me process that is what is the optimal leg of Q What is optimal lack of a model which is denoted by q optimal Never fear models denoted by P and optimal lack of every models unit A q or an Arma process it is what are the values of p and q or an animal process.

So, in this case, we must know the values of p d and Q where p is the optimal level of AR model, these are differencing Q's optimal level MMO the BGM Raji comes in handy in answering the preceding question, so, it helps us in identifying the optimal lags of p, d and Q this method consists of four steps. So, let's move to the first step The first step is identification where we are identifying the optimal lags of AR model in a model order differencing. First, let's identify the optimal length of AR model optimal lines of air modal is identified by psdf graph or partial autocorrelation function graph. So, what is partial autocorrelation function? partial autocorrelation function at lackey is the correlation between time series values that are key intervals apart accounting for the values of the intervals between two that is the partial autocorrelation function which is used to identify the optimal lag of ER model that is p Then we have to identify the optimal lag of a model that is q optimal lag of a modeler Q is identified using autocorrelation function graph.

So, what is autocorrelation function autocorrelation function at lackey is the correlation between time series values that are key intervals apart Q is the optimal lag of a model PS optimal lag of AR model then we identify the order of difference in that is the number of times differencing has to be done with the time series model to restore station here the ACF function and the PC function that is the ACF graph and the PC graph are represented graphically and we also need to remember that ACF graph and PC graph are together called Carrillo crumbs. Let's move to the next step after identification comes estimation that is we have to After identifying the parameters of animal model that is p d and q that is optimal level of error model of an order differencing. an optimal level of a model we have to estimate the parameters for autoregressive moving average terms this parameter estimation is done using software the techniques that are used maximum likelihood estimation or conditional least squares Let us to estimate the parameters for Ross Jenkins technology that is estimating the parameters for Arima model in boxes using the box Jenkins technology that is the parameters for autoregressive moving average terms the next step is diagnostic checking diagnostic checking having estimated the parameters we then choose whether our model is a good fit or not, whether the model is fitted well or not, we also do an L jam box test under diagnostic checking we also check whether the optimum labs that we have calcul identified are optimal or not we do edge on box test that is done for diagnostic check where my h note on our hypothesis is the data is identical independently distributed that is data is ID and each one alternative hypothesis data is not identically and independently distributed.

And after estimating the different parameters of autoregressive that is autoregressive parameters moving average parameters after doing diagnostic checking then other than identification that is identifying the different parameters of animal model that is optimal Software model optimal observe any model that is P and Q then often after calculating the order of differencing that is the number of times differencing is done to restore stationarity the last step that is our actual objective is forecasting. That is, we use the present time series data predict the future values using the model. So, before I move to the next video or before I stop this video over here, let me recap the concepts that we have learned till here we have learned the different concept of time series the concepts of time series The different assumptions of time series The different applications of time series analysis, the key differences between time series data cross sectional data and panel data the different components of time series, The stationarity non stationary part of time series data stationarity is when the mean and variance of a time series data is constant non stationarity is mean and variance of time series data are not constant for smoothing techniques that are adopted to reduce the random variations of time series data the techniques that are adopted to convert the non stationary data to stationary that is the detaining technique and the differences technique 10 we are able to talk about Arima modeling which is used to do forecasting Arima model is composed of a RNN model and auto integration er is an autoregressive model where the dependent variable is the function of his own past values and moving average model is the function of the lagged values of their terms and their terms of the time period order with integration is the number of times differencing is done to restore stationarity of our time series data, we have identified the optimal lags of a model in order differencing using the BJs technology where optimal lags of our model is identified or is denoted as P and optimal as of no more design debate from PCA graph that is partial autocorrelation function.

Optimal lines of a model is identified from a graph that is auto correlation function graph, we have also identified the order of differencing there is a number of times differencing has to be done to restore stationarity of our time series data we had discussed about the BJs technology there is option kins technology which is used for animal modeling the footsteps of box Jenkins technology the identification identification is the first step Nexus estimation where we are estimating the parameters for m that is a autoregressive parameters and the moving average parameters using the maximum likelihood estimation are conditionally squares estimate conditionally squares there is maximum likelihood estimation technique or condition these first technique is used to estimate the parameters for animal modeling, then we have done diagnostic checks to check whether our model is a good fit or not to check whether the labs that we have identified are optimal or not, we also do a jump box test to check whether the data is equal to ID or not with the H not null hypothesis is the data is equal to it that is it is identically independently distributed in each one alternative hypotheses data is not it that is it is not identical independently distributed and then after estimating the different parameters and after checking whether the model is a good fit or not after estimating the different coefficients we are doing the forecasting.

Now, before I stop this video, let me know let me tell you all the concepts that we are going to do in the next video. In the next video we will be discussing about the case study and the data set that we'll be using to do time series analysis in SAS. For now, let's end this video over here. Goodbye. Thank you and see you all for the next video.