Time-series forecasting Flashcards
Importance of forecasting
Governments forecast unemployment, interest rates and expected revenues from income taxes for policy purposes.
Marketing executives forecast demand, sales and consumer preferences for strategic planning.
University administrators forecast enrolments to plan for facilities and for faculty recruitment.
Retail stores forecast demand to control inventory levels, hire employees and provide training.
Time-series data and plot
Numerical data obtained at regular time intervals.
The time intervals can be annually, quarterly, daily, hourly etc.
A time-series plot is a two-dimensional plot of time series data.
The vertical axis measures the variable of interest.
The horizontal axis corresponds to the time periods.
Classical Multiplicative Time-series Model Components
Trend component
Seasonal component
Cyclical component
Irregular component
Trend component
Long-run increase or decrease over time (overall upward or downward movement).
Data taken over a long period of time.
Trend can be upward or downward.
Trend can be linear or non-linear.
Seasonal component
Short-term regular wave-like patterns.
Observed within 1 year.
Often monthly or quarterly.
Cyclical component
Long-term wave-like patterns.
Usually occur every 2-10 years.
Often measured peak to peak or trough to trough.
Irregular component
Unpredictable, random, ‘residual’ fluctuations.
Due to random variations of:
Nature.
Accidents or unusual events.
‘Noise’ in the time series.
Usually short duration and non-repeating.
Smoothing the Annual Time Series – Moving Averages
A series of arithmetic means over time.
Calculate moving averages to get an overall impression of the pattern of movement over time.
Moving averages can be used for smoothing: averages of consecutive time-series values for a chosen period of length (L).
Result dependent upon choice of L (length of period for computing means).
Examples:
For a 5 year moving average, L = 5.
For a 7 year moving average, L = 7 etc.
Choosing a Forecasting Model
Perform a residual analysis:
look for pattern or direction.
Measure magnitude of residual error:
using squared differences.
using absolute differences.
Use simplest model:
principle of parsimony.
The Principle of Parsimony
Suppose two or more models provide a good fit for the data.
Select the simplest model. Simplest model types: Least-squares linear Least-squares quadratic 1st order autoregressive. More complex types: 2nd and pth order autoregressive Least-squares exponential Holt-Winters.
Pitfalls in Time-series Analysis
Assuming the mechanism that governs the time-series behaviour in the past will still hold in the future.
Using mechanical extrapolation of the trend to forecast the future without considering personal judgements, business experiences, changing technologies, and changing habits.
COMMON APPROACHES TO FORECASTING
1
TIME SERIES DATA AND PLOT
2
TREND COMPONENT
3
SEASONAL COMPONENT
4
Multiplicative Time-series Model for Annual Data
5
Multiplicative Time-series Model with Seasonal Component
6
Moving averages
7-10
LEAST SQUARES TREND FITTING
11
NON LINDEAR TREND FORECASTING
12 SQUARE THE XI’S LOOK AT 11 AND SQUARE THE X
EXPONENTIAL TREND MODEL
13-14 (SIMPLE LINEAR REGRESSION WITH LOGS)
MODEL SELECTION
15-16
RESIDUAL ANALYSIS
17 RANDOM ERRORS IS GOOD
MEASURING ERRORS
18
FORECASTING WITH SEASONAL DATA
19
Exponential Model with Quarterly Data
20 MULTIPLE REGRESSION
ESTIMATING THE QUARTERLY MODEL
21
QUARTERLY MODEL EXAMPLE
22-23
