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.

> msft_ar<-arima(msft_ts,c(1,0,0))

### 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 60.29762 $se Time Series: Start = 253 End = 272 Frequency = 1 [1] 0.7675185 1.0754465 1.3051026 1.4933081 1.6544932 1.7961449 [7] 1.9227626 2.0373125 2.1418796 2.2379995 2.3268456 2.4093400 [13] 2.4862246 2.5581077 2.6254964 2.6888192 2.7484426 2.8046829 [19] 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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