11_mich_Lecture 11 Slides_awap

Chart 1 -White Noise
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Chart 2 - Unemployment Rate (%)
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Follow-up reading: Wooldridge Chapters 10.1,11.1 S & W Chapters 14.1,14.2
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Chart 1A – ACF: White Noise
1 0.8 0.6 0.4 0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 -0.2 -0.4 -0.6 -0.8 -1 ACF White Noise Upper bound Lower bound
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The correlogram
The plot of autocorrelations against (the lag) gives the plot of the autocorrelation function (or acf) This plot is known as the correlogram The maximum lag K considered in plotting the acf should be /3 The shape of the plotted acf can show important time series properties For a white noise series (random sample) , 0 Hence the theoretical acf is flat at zero. For a sample time series actual values will be non-zero, but ~ 0,1/
Interpreting the correlogram
Treat as significantly different from 0 if | | 2/ , but ignore single significant values unless they are at economically meaningful lags If the series is not white noise these bounds ‘fan out’ ~ 0, 1
Univariate time series analysis
A single time series is explained by its own past history, and not by exogenous variables (as in linear regression) Such explanations are limited, but they • provide a framework for analysing the statistical properties of time series regressions • provide a benchmark against which we can evaluate regression models • can often suggest how a regression model of time series data should be designed
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Motivations for time series analysis - 2
• Diagnostic tests – the regression residuals be unpredictable should
some regressions can be discarded as ‘spurious’ because the residuals have undesirable properties
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Chart 3 - ln real GDP
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Describing a time series - the autocorrelation function
Suppose we want to describe how observations which are ‘close’ in time are related We measure the relationship between adjacent observations using the 1st-order autocorrelation coefficient , , / Higher-order autocorrelation coefficients are defined by , / We know that 1 1
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Graphical analysis of time series
Economic time series do not look as if they are generated by random sampling A random sample has moments 0 Artificial time series constructed using these rules are called ‘white noise’. For a white noise series cannot be predicted from its past history For a typical economic series, a time series plot suggests that the past history of the series can be used to predict future values ,
Characteristics of time series - 2
• Stationary time series The nature of the process does not depend on when it is observed Mean daily outside temperature in Cambridge (annual variation) APC for population in equilibrium at different dates (this is suggested by PIH) • Nonstationary time series Key characteristics of the series depend on when process is observed Population of Cambridge GDP and other macroeconomic aggregates Share prices (and other speculative asset prices)
– knowing the time series properties of help design of regression models
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fitting a linear trend to log GDP gives systematic residuals this has implications for how we should model GDP
Introduction to time series analysis
In many cases (especially in macroeconomics) a sample consists of a set of observations measured over time Such data cannot be treated as a random sample - in fact we need new concept of population and sample In time series data the order (not the ‘label’) of the observations matters Means, variances, covariances do not depend on order: since summary statistics and regression do not use order information, this suggest that they need to be supplemented by other information
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Chart 5 - ln Bond Yield
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ln Bond Yield
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Chart 6 - Consumer durables (share of total)
changes in the exchange rate should not be predictable