Forecasting with AutoRegressive (AR) Model in R
Now that we know how to estimate the AR model using ARIMA, we can create a simple forecast based on the model.
Step 1: Fit the model
The first step is to fit the model as
ARIMA(1, 0, 0). We have already seen this in the previous lesson.
Step 2: Create Forecast
We can now use the
predict() function to create a forecast using the fitted AR model. It takes as its inputs, the model object that we created in step 1, and an additional parameter
n.ahead which establishes the forecast horizon, that is, how many steps (periods) in the future we want to create the forecast. In our example, we will provide
n.ahead=20, which will create forecast for next 20 steps which corresponds to 20 days for our daily data.
> msft_forecast <- predict(msft_ar, n.ahead = 20)
The object generated by the
predict() command contains two time series: 1)
$pred which contains the forecasted values and 2)
$se which contains the standard error for the forecast. We will use the
$pred time series to plot the forecast and the
$se time series to add confidence intervals to our plot.
> msft_forecast pred Time Series: Start = 253 End = 272 Frequency = 1 \[1\] 62.03064 61.92331 61.81796 61.71456 61.61307 61.51346 61.41569 \[8\] 61.31973 61.22554 61.13309 61.04236 60.95330 60.86588 60.78009 \[15\] 60.69588 60.61323 60.53210 60.45248 60.37432 60.29762se Time Series: Start = 253 End = 272 Frequency = 1  0.7675185 1.0754465 1.3051026 1.4933081 1.6544932 1.7961449  1.9227626 2.0373125 2.1418796 2.2379995 2.3268456 2.4093400  2.4862246 2.5581077 2.6254964 2.6888192 2.7484426 2.8046829  2.8578161 2.9080845
For simplicity sake, let's also extract the two series in their own respective variables.
> msft_forecast_values <- msft_forecast$pred
msft_forecast_se <- msft_forecast$se
Step 3: Plot the Forecast
We can now use the
plot.ts() function to first plot the original data and then add points for the forecasted values using the
points() function as shown below:
> plot.ts(msft_ts, xlim = c(0, 300), ylim = c(40,80))
points(msft_forecast_values , type = "l", col = 2)
Notice that while creating the initial plot, we've specified scale limits for x and y axis in order to provision for the forecast values.
Step 4: Add Confidence Intervals to Forecast
We can add a 95% confidence interval to our forecast using the standard error values.
> points(msft_forecast_values - 2*msft_forecast_se, type = "l", col = 4, lty = 2)
points(msft_forecast_values + 2*msft_forecast_se, type = "l", col = 4, lty = 2)
You have successfully created your first forecast.
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- 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