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Moving Average (MA) Model in R

Data Science

This lesson is part 21 of 27 in the course Financial Time Series Analysis in R

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 xt 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.

# 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.

> acf(MA_1)
> pacf(MA_1)
Previous Lesson

‹ Forecasting with AutoRegressive (AR) Model in R

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Estimating Moving Average (MA) Model in R ›

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In this Course

  • Financial Time Series Data
  • Exploring Time Series Data in R
  • Plotting Time Series in R
  • Handling Missing Values in Time Series
  • Creating a Time Series Object in R
  • Check if an object is a time series object in R
  • Plotting Financial Time Series Data (Multiple Columns) in R
  • Characteristics of Time Series
  • Stationary Process in Time Series
  • Transforming a Series to Stationary
  • Time Series Transformation in R
  • Differencing and Log Transformation
  • Autocorrelation in R
  • Time Series Models
  • ARIMA Modeling
  • Simulate White Noise (WN) in R
  • Simulate Random Walk (RW) in R
  • AutoRegressive (AR) Model in R
  • Estimating AutoRegressive (AR) Model in R
  • Forecasting with AutoRegressive (AR) Model in R
  • Moving Average (MA) Model in R
  • Estimating Moving Average (MA) Model in R
  • ARIMA Modelling in R
  • ARIMA Modelling – Identify Model for a Time Series
  • Forecasting with ARIMA Modeling in R – Case Study
  • Automatic Identification of Model Using auto.arima() Function in R
  • Financial Time Series in R – Course Conclusion

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