In this video we will be talking about Arima modeling what is Arima modeling and Arima model is a class of statistical models for analyzing and forecasting time series data it explicitly caters to suit of standard structures in time series data and as such provides a simple yet powerful method for making skillful time series forecasts. erima is an acronym that stands for autoregressive integrated moving average, it is a generalization of the simpler autoregressive moving average and adds the notion of integration. So, full form of itemized autoregressive integrated moving average model before proceeding to discuss the ARIMA models it is necessary to note that the forecasting methods that we are going to discuss assume that the underlying time series are stationary or they can be made stationary with appropriate transformations. So, as we Know that in order to do forecasting on our time series data, we have to convert the data from non stationary to stationary and we are applying Arima model to forecast the future values.

So, the sufficient the necessary condition the necessary condition for applying Arima modeling to our data is the data should be first the time series data should be first stationary and if it is non stationary we have to convert into this stationary by adopting different techniques and taking appropriate transformations. Further animal models can be constructed both for a single time series as well as for a multivariate time series while the former is known as a univariate Arima model. The latter is called the multivariate ARIMA models. Now, the concept of animal model is represented graphically over here here the animal model I've represented it graphically. So, this is the graph for animal model. Now, the Arima model stands for auto regressive integrated moving average model.

So, when we are talking about animal model there are certain key aspects which comes along with it. The first aspect that we are going to talk about is the autoregressive model or the AR mode. Now, what is autoregressive model or the AR model, our time series model is said to be auto regressive in nature if the value of the dependent variable is a function of its own past values, that is a model that uses the dependent relationship between an observation and some number of lagged observations. So, this is the equation for our autoregressive model or AR model that is the equation of a process is x equals to row one x two minus one plus row two x two plus row three x two minus three plus rho nx two minus n plus et where extraneous one extra ministry extra ministry learn extra extra men as men are the lab values that is up to an eight lakh row of the absolute value of row if it is less than one This implies stationarity which shows that the errors are dying down gradually it is the error terms or the time period and row one row two row $3 ruin these art that is row is my autoregressive coefficient.

This is row one is the coefficient of XT minus one presumption of extra ministry and role is the autoregressive coefficient x is the value of the dependent variable at a time period. Now let's move to the next aspect of animal model that is a model or the moving average model. In this the time series model is dependent on the past and the current values of the error terms, that is of the model that uses the dependency between an observation and residual error from a moving average model applied to lagged observations. So here my dependent variable is the function of its of the lagged values of the error terms in our model or autoregressive model, the dependent variable that was the function of its own past values and here in a model are the moving average model the dependent variable is a function of its present value of the error terms and the past values of the error terms.

So here the time lags are with respect to the error terms here theta is a moving average coefficient and eta minus one at ministry, t three t minus three, these are the timelapse up to keep nuts for me models. So you Your n is the optimal lack of air model and case optimal level of ma model. Now, let's move the animal model animal model is basically an ARMA model which is tested for stationarity. And in order to convert data from non stationary to stationary that is to destroy stationarity the technique that is used is differencing technique, the number of times differencing is done in order to restore stationarity is the order of differencing. For Arima model the order of integration is basically the number of times differencing is done to destroy stationarity. So, the order of integration the order differences seem so, the parameters of the Arima model are as follows that is the P which stands for document lines of AR model D is order differencing there is a number of times a differencing has to be done to ensure stationarity and choose the optimal lags of ma model.

So, we will be learning till here in this video so now in our next video we'll be discussing about box Jenkins technology which is used to do animal modeling and the various tips box Jenkins technology that is identification estimation diagnostic check and focused So for now, let me end this video over here. Goodbye. Thank you see you all for the next video.