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Time Series Models for Business and Economic Forecasting

Hung-Pin LaiMarch 18, 2007

The six key features of economic time series

• Trends• Seasonality• Somehow influential data points (aberrant

observations)• A variance that changes because of past

observations (conditional heteroskedasticity)• non-linearity• Common features

Many time series data have at least one of the first five features:

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1. Trends

Modeling trend

• By a Linear trend

• Use growth rate

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Changing trends

• 1946-1960increasing trend

• 1960-1973decreasing trend

• 1974 --upward again

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2. SeasonalityObservations in certain seasons display strikingly different features to those in other Seasons.

Modeling seasonality

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(See figure 2.3 for the original data)

R2=0.296

R2=0.254

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R2=0.971

R2=0.965

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(increasing variance; changing seasonality)

(mean shift; regime shift; structural break)

television

radio

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3. Aberrant observationDefinition: When a single observation have a major impact on time series modeling and forecasting, it is called aberrant observation.

yt =log(pricet)

Features of Figure 2.11:

1. The differenced yt is not a good approximation to the inflation when the quarterly inflation rate is high.

2. The data in 1989 (extreme value) seem to be quite different from those observations the years before. Consider the model:

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4. Conditional heteroskedasticity

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Aberrant observations tend to emerge in clustersClusters of observations with large variances(volatility clustering or conditional heteroskedasticity)

Modeling conditional heteroskedasticity:

5. Non-linearityEverything other than nonlinearityRegime switching or state dependency

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Modeling regime switching:

• Model

6. Common featuresCommon trend (cointegration); common seasonality, Multivariate models

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