A Moving Average is a process where each value is a function of the noise in the past observations. These are the random error terms which follow a white noise process. The general form is MA(q), where x_{t} depends on q past values.

Just like AR models, this also has a regression like structure, however, instead of the actual values, we are regressing each value on the noise/error in the previous observations.

We can use the `arima.sim()`

function to simulate the MA model. For the MA model, we will specify model as `list(ma = theta)`

, where theta is the slope parameter from the interval (-1, 1).

Below we create two sets of simulations with MA model, one with a slope of 0.5 and another with a slope of 0.8.

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# Simulate AutoRegressive model with 0.5 slope MA_1 <- arima.sim(model = list(ma = 0.5), n = 200) # Simulate AutoRegressive model with 0.8 slope MA_2 <- arima.sim(model = list(ma = 0.9), n = 200) # Simulate AutoRegressive model with -0.6 slope MA_3 <- arima.sim(model = list(ma = -0.6), n = 200) plot.ts(cbind(MA_1 , MA_2, MA_3 ), main="MA Model Simulated Data") |

### ACF and PACF of Autoregressive Model

We can calculate the Autocorrelation and Partial Autocorrelation functions of the Moving Average model using the `acf()`

and the `pacf()`

functions.

The following are the respective ACF and PACF plots for the `MA_1`

series.

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> acf(MA_1) > pacf(MA_1) |

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