Confidence Intervals for Forecast

Your forecast object forecast_MET_t not only has the forecast, but also margin of error calculations for the forecast called confidence intervals. These confidence intervals show us a wiggle room on our forecasts since no forecast is ever perfect.

The forecast was stored as the object forecast_MET_t$mean. The upper and lower limit of this interval is stored similarly. The second column of the upper confidence interval is the 95% confidence interval and can be accessed via forecast_MET_t$upper[,2]. To get the lower limit replace the word upper with lower.

This exercise is part of the course

Forecasting Product Demand in R

Exercise instructions

Convert both the upper and lower 95% confidence limits to xts objects upper and lower. Your date index is stored as for_dates.
Add these to the plot of the forecast and the validation data set.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Plot the validation data set
plot(MET_t_valid, main = 'Forecast Comparison', ylim = c(4000, 8500))

# Overlay the forecast of 2017
lines(for_MET_t_xts, col = "blue")

# Convert the limits to xts objects
lower <- xts(forecast_MET_t$___[,2], order.by = ___)
upper <- xts(___$___[,___], order.by = for_dates)

# Adding confidence intervals of forecast to plot
lines(lower, col = "blue", lty = "dashed")
lines(___, col = "blue", lty = "dashed")

Edit and Run Code

This exercise is part of the course

Forecasting Product Demand in R

IntermediateSkill Level

4.8+

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When it comes to forecasting, time series modeling is a great place to start! You need to forecast out the future values of sales demand and a good baseline approach would be ARIMA models. In this chapter you'll learn how to quickly implement ARIMA models and get good initial forecasts for future product demand.

Exercise 1: Loading data into xts object Exercise 2: Importing data Exercise 3: Plotting / visualizing data Exercise 4: ARIMA Time Series 101 Exercise 5: auto.arima() function Exercise 6: Interpret auto.arima Exercise 7: Forecasting and Evaluating Exercise 8: Forecast function Exercise 9: Calculating MAPE and MAE Exercise 10: Visualizing Forecast Exercise 11: Confidence Intervals for Forecast

Current Exercise

Economic theory has a lot to say about predicting values of demand. Obviously, external factors like price, seasonality, and timing of promotions will drive some aspects of product demand. In this chapter you'll learn about the basics around price elasticity models and how to incorporate seasonality and promotion timing factors into our product demand forecasts.

Exercise 1: Price elasticity Exercise 2: Calculating price elasticity Exercise 3: Interpret results from elasticity Exercise 4: Seasonal / holiday / promotional effects Exercise 5: Visualize holiday / promotion effects Exercise 6: Create holiday / promotional effect variables Exercise 7: Regression for holiday / promotional effects Exercise 8: Significant holiday or promotional effects?Exercise 9: Forecasting with regression Exercise 10: Create future predictor variables Exercise 11: Forecast future values of demand Exercise 12: Visualizing forecasts of regression

Time series models and pricing regressions don't have to be thought of as separate approaches to product demand forecasting. They can be combined! In this chapter you'll learn about two ways of "combining" the information gained in both modeling approaches - transfer functions and forecast ensembling.

Exercise 1: Residuals from regression model Exercise 2: Calculating residuals from regression Exercise 3: Visualizing residuals Exercise 4: Forecasting residuals Exercise 5: auto.arima function Exercise 6: Forecasting residuals with time series Exercise 7: Visualizing residual forecasts Exercise 8: Transfer functions & ensembling Exercise 9: Combining residuals from regression & time series Exercise 10: Visualizing transfer function forecast Exercise 11: Calculating transfer function MAPE and MAE Exercise 12: ARIMA Forecasting Exercise 13: Ensembling of Forecasts

Everything up until this point deals with making individual models for forecasting product demand. However, we haven't taken advantage of the fact that all of these products form a product hierarchy of sales. Products make up regions and regions make up states. How can we ensure that our forecasts reconcile correctly up and down the hierarchy? In this chapter you'll learn about hierarchical forecasting and how to use it to your advantage in forecasting product demand.

Exercise 1: Bottom-Up Hierarchical Forecasting Exercise 2: Build time series forecast for new product Exercise 3: Build regression forecast for new product Exercise 4: Ensemble forecast for new product Exercise 5: Calculate bottom-up forecast for whole region Exercise 6: Top-Down Hierarchical Forecasting Exercise 7: Build time series forecast at regional level Exercise 8: Using average historical proportions Exercise 9: Using proportion of historical averages Exercise 10: Middle-Out Hierarchical Forecasting Exercise 11: Build time series forecast for new region Exercise 12: Top-down forecast for new region Exercise 13: Bottom-up forecast for whole state Exercise 14: Congratulations!