Notes on Chapter 1 of Forecasting: Principles & Practice
What can be forecast#
Factors that affect the predictability of an event or a quantity
- How well we understand the factors that contribute to it;
- How much data is available;
- How similar the future is to the past;
- Whether the forecasts can affect the thing we are trying to forecast.
Example 1: Short-term forecasts of residential electricity demand
- Temperature is a primary driving force of the demand, especially in summer.
- Historical electricity usage data is available.
- It’s safe to assume that the demand behavior will be similar to that in the past. I.e., there is some degree of seasonality.
- Price of the electricity is not strongly dependent on the demand. So the forecast will not have too much effect on consumer behavior.
Example 2: Currency exchange rate
- We have very limited knowledge about what really contributes to exchange rates.
- There is indeed a lot of historical exchange rate data available.
- Very difficult to say that the future will be similar to the past. The market is very sensitive to a number of unpredictable factors such as political situation, a country’s financial stability and economy policies, … etc.
- The exchange rate is bound to have strong correlation to the forecast outcome, as the market will response to any forecast results. This is called the efficient market hypothesis.
Based on the predictability criterion, the exchange rate is likely not predictable. In fact, things like stock price and lottery number fall in this category.
Determine what to forecast#
It is necessary to consider the forecasting horizon. Will it be one month in advance, 6 months, or for multiple years. Depending on the forecast horizon, different types of models will be necessary.
Forecasting data and methods#
- Qualitative forecasting: If there are no data available, or the data are not relevant to the forecast.
- Quantitative forecasting can be applied when:
- Numerical information about the past is available.
- It is reasonable to assume that some aspects of the past patterns will continue into the future.
Forecasting models#
Explanatory model: In this scenario, the historical behavior of a time series is assumed to be captured by the so-called predictor variables. For example, the hourly electricity demand \(d\) of a hot region during summer can be modeled by $$ d = F(\text{temperature}, \text{population}, \text{time of day}, \text{day of week}, \text{error} ). $$
The relationship is not exact, but these variables are primary factors that are likely to impact the electricity demand. This type of model explains what causes the variation in electricity demand.
Time series model: Electricity demand data form a time series. Hence a time series model can be used for forecasting. In this case, the demand \(d_{t+1}\) at time \(t+1\) is expressed as follows $$ d_{t+1} = F(d_t, d_{t-1}, d_{t-2}, \ldots, \text{error}), $$ where \(t\) represents the current hour, \(t+1\) is the next hour, \(t-1\) is the previous hour, and so on. The prediction of the future is based on past values of a variable but not on external variables that may affect the system.
Mixed models: The combination of the above two models $$ d_{t+1} = F( d_t, \text{temperature}, \text{population}, \text{time of day}, \ldots, \text{error}), $$