Question

Explain in depth the stationarity conditions for autoregressive (AR) model and moving average (MA) models.

Answer 1

In statistics in signal processing and autoregressive model representation of a common type of random process as such it is used to describe certain time varying processes in nature economics the autoregressive model specifies that the output variables depend linearly on its own previous values on a stochastic term does the model is in the form of different equation together with the moving average model it is a special case and the key component of the more general models of time series which have more complicated structure it is also a special case of vector autoregressive model which consists of system of more than interlocking difference equation more than 1 evolving random variable

Estimation of auto variances and autocorrelation formulation as at least squares regression problem evaluating the quality of forecast for predictive performance of auto oppressive model can be accessed as soon as estimation has been done if cross validation is used in the sum of the initial available data was used for parameter estimation purposes and some was held for out of Sampling testing alternatively after some time has passed after the parameter estimation was conducted more data will become available and predictive performance can be evaluated by using the new data.

Moving average model in the time series analysis is a common approach to modelling univariate time series the moon moving average model specifies that the output variable depends linearly on the current and various pass values ok IM perfectly predictable term the moving average model is essentially a finite impulse response filter applied to white noise with some additional interpretation interpretation placed on it the role of the random shops in the model differs from their role in the autoregressive model in two ways firstly they are propagated to future values of the time series directly and secondly they are different in methods.