What is the variance of a ma Q process?

The mean and variance of any MA(q ) process are finite and constant, while the autocorrelation function is finite and does not depend on t . Therefore any MA(q ) is weakly stationary. The autocorrelation function of an MA(q ) process is positive at lags 1,…,q and zero for any lag greater than q .

How is autocovariance function derived?

To calculate the autocovariance function, we first calculate Cov[X[m],X[n]] Cov [ X [ m ] , X [ n ] ] assuming m . Since X[n]=Z[1]+Z[2]+… +Z[n], + Z [ n ] , we can write this as Cov[X[m],X[n]]=Cov[Z[1]+…

What is a ma process?

In time series analysis, the moving-average model (MA model), also known as moving-average process, is a common approach for modeling univariate time series. Contrary to the AR model, the finite MA model is always stationary.

What is moving average processes?

In statistics, a moving average is a calculation used to analyze data points by creating a series of averages of different subsets of the full data set. In finance, a moving average (MA) is a stock indicator that is commonly used in technical analysis.

What is autocovariance function for moving average models?

For an MA(1), the autocovariance function truncates (i.e., it is zero) after lag 1. Al Nosedal University of Toronto The Moving Average Models MA(1) and MA(2) February 5, 2019 7 / 47 The Autocorrelation for MA(1) Models ˆ(0) = (0) (0) = 1: ˆ(1) = (1) (0) = b 1 + b2 : ˆ(k) = 0 for all k >1:

Which is the formula for the moving average process?

A \\frst-order moving-average process, written as MA(1), has the general equation x t= w t+ bw t 1 where w tis a white-noise series distributed with constant variance ˙2 w. Al Nosedal University of Toronto The Moving Average Models MA(1) and MA(2) February 5, 2019 2 / 47 The Autocovariance for MA(1) Models

How to calculate autocorrelation for moving average models?

The Autocorrelation for MA(1) Models ˆ(0) = (0) (0) = 1: ˆ(1) = (1) (0) = b 1 + b2 : ˆ(k) = 0 for all k >1: Al Nosedal University of Toronto The Moving Average Models MA(1) and MA(2) February 5, 2019 8 / 47 The Autocovariance for MA(q) Models

How to calculate autocovariance for Ma ( Q ) models?

The Autocovariance for MA(q) Models For the qth-order MA process, we can use a similar derivation to show that the autocovariance function, (k), truncates after lag q. Once again (k) = E(x tx t k) Al Nosedal University of Toronto The Moving Average Models MA(1) and MA(2) February 5, 2019 9 / 47 The Autocovariance for MA(q) Models