Time Series Analysis and Forecasting in Practice
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This document discusses time series analysis and forecasting. It covers the components of time series including trends, seasonality, cyclical patterns and irregular components. It then describes several approaches to forecasting including qualitative judgmental methods, statistical time series models and explanatory causal models. Specific statistical time series forecasting techniques are explained such as simple and exponential smoothing, linear regression models, and Holt-Winters seasonal models. The importance of evaluating forecast accuracy is also highlighted.
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Time Series Analysis and Forecasting in Practice
- 1. Time Series Analysis & Forecasting CS5122 DESCRIPTIVE & PREDICTIVE ANALYTICS DILUM BANDARA [email protected] Some slides adapted from business analytics: Methods, models, and decisions, 1st edition by James R. Evans
- 2. Example - Monthly International Airline Passengers Source: Time Series Analysis: Forecasting and Control by Box and Jenkins (1976) 2
- 3. Example – Human Electrocardiogram (ECG) Source: Time Series Analysis by N. Janson 3 time voltage ~ 1 sec
- 4. System, Process, & Signal Source: Time Series Analysis by N. Janson A collection of observations of state variables made sequentially in time ◦ Can be Univariate, Bivariate, or Multivariate 4 System State variable 1 State variable 2 Signals
- 5. Time-Series Components 5 Time Series Cyclical Component Irregular Component Trend Component Seasonal Component Overall, persistent, long- term movement Regular periodic fluctuations, usually within a day or 12-month period Repeating swings or movements over more than one year Erratic or residual fluctuations
- 6. Trend Component 6 Sales Time Downward linear trend Sales Time Upward nonlinear trend Time Sales
- 9. Forecasting Managers require good forecasts of future event(s) Business Analysts may choose from a wide range of forecasting techniques to support decision making 3 major forecasting approaches 1. Qualitative & judgmental techniques 2. Statistical time-series models 3. Explanatory/causal models 9
- 10. 3 Major Forecasting Approaches Used when historical data are unavailable Considered highly subjective and judgmental Common Approaches to Forecasting Causal Quantitative forecasting methods Qualitative forecasting methods Time Series Use past data to predict future values 10
- 11. Qualitative & Judgmental Forecasting Rely on experience & intuition They are necessary when historical data is not available or when predictions are needed far into the future Historical analogy approach obtains a forecast through comparative analysis with prior situations Delphi method questions an anonymous panel of experts 2-3 times in order to reach a convergence of opinion on forecasted variable 11
- 12. Example – Predicting Price of Oil Early 1988 – oil price was about $22 a barrel Mid-1988 – oil price dropped to $11 a barrel Price decrease due to oversupply/lower demand OPEC eventually reduced supply In 2000 – price rose to $27 Late 2001 – price dropped to $23 12
- 13. Example – Natural Gas Usage 13
- 14. Statistical Forecasting Models Simple Models 1. Simple Moving Average (SMA) 2. Simple Exponential Smoothing Time Series with Linear Trends 1. Double moving average 2. Double exponential smoothing 3. Simple linear regression These are based on the linear trend equation Ft+k = at + bt k Forecast for k periods into the future is a function of level at and the trend bt Models differ in their computations of at and bt 14
- 15. Simple Moving Average (SMA) Method A smoothing method Averages random fluctuations in a times series Assumes future observations will be similar to the recent past A k-period (window) moving average averages the most recent k observations Larger k results in smoother forecast models 15
- 16. Example – Annual Data 16 Year Sales 1 2 3 4 5 6 7 8 9 10 11 etc… 23 40 25 27 32 48 33 37 37 50 40 etc… Annual Sales 0 10 20 30 40 50 60 1 2 3 4 5 6 7 8 9 10 11 Year Sales
- 17. Example – Annual Data (Cont.) 17 Each moving average is for a consecutive block of 5 years Year Sales 1 23 2 40 3 25 4 27 5 32 6 48 7 33 8 37 9 37 10 50 11 40 Average Year 5-Year Moving Average 3 29.4 4 34.4 5 33.0 6 35.4 7 37.4 8 41.0 9 39.4 … … 5 5 4 3 2 1 3 5 32 27 25 40 23 29.4
- 18. Example – Annual Data (Cont.) 5-year moving average smoothers data & makes it easier to see the underlying trend 18 Annual vs. 5-Year Moving Average 0 10 20 30 40 50 60 1 2 3 4 5 6 7 8 9 10 11 Year Sales Annual 5-Year Moving Average
- 19. Simple Exponential Smoothing Method α – smoothing constant between 0 and 1 α close to 0 – biased to past, capture long-term trend α close to 1 – biased to present, respond quickly 19
- 20. Error Metrics to Compare Forecasts 20 Mean Absolute Deviation Root Mean Squared Error Mean Squared Error Mean absolute % Error
- 21. Linear Trends Forecasting 21 Double Exponential Smoothing of Coal Production data 1960-2007 Linear Regression of Coal Production data X b b Ŷ 1 0
- 22. Forecasting Models with Seasonality 1. Linear Regression using dummy variables 2. Holt-Winters models 1. Additive – stable seasonality 2. Multiplicative – amplitude changes over time 3 parameters are use to smooth: level, α trend, β seasonality, γ 22 Forecasting Natural Gas Usage Using Holt-Winters No-Trend Model
- 23. Capturing Seasonality & Trend 23
- 24. Autoregressive Modeling Takes advantage of autocorrelation ◦ 1st order - correlation between consecutive values ◦ 2nd order - correlation between values 2 periods apart pth order Autoregressive model 24 i p - i p 2 - i 2 1 - i 1 0 i Y A Y A Y A A Y δ Random Error
- 25. Forecasting with Causal Variables Sales of fuel is influenced by fuel price Predict gasoline sales using both time & price per gallon ◦ Price per gallon is a causal variable ◦ Causal or explanatory variables may influence the time series 25
- 26. Forecasting in Practice Judgmental & Qualitative methods are used for forecasting sales of product lines & broad company & industry forecasts. Simple time-series models are used for short- & medium- range forecasts. Regression methods are typically used for long-term forecasts Beware of: ◦ Assuming mechanism that governs the time series behavior in the past will still hold in the future ◦ Using mechanical extrapolation of trend to forecast future without considering personal judgments, business experiences, changing technologies, & habits 26