Not be done using acfs we want to form a parsimonious

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Unformatted text preview: it to data specific features • This gives motivation for using information criteria, which embody 2 factors - a term which is a function of the RSS - some penalty for adding extra parameters The object is to choose the number of parameters which minimizes the information criterion. • 40 Information Criteria for Model Selection • • • The information criteria vary according to how stiff the penalty term is. The three most popular criteria are Akaike’s (1974) information criterion (AIC), Schwarz’s (1978) Bayesian information criterion (SBIC), and the Hannan-Quinn criterion (HQIC). where k = p + q + 1, T = sample size. So we min. IC s.t. SBIC embodies a stiffer penalty term than AIC. Which IC should be preferred if they suggest different model orders? – SBIC is strongly consistent but (inefficient). – AIC is not consistent, and will typically pick “bigger” models. 41 Forecasting in Econometrics • Forecasting = Prediction. Forecasts are made to guide decisions in a variety of fields. Economics: The forecast of the major economic variables, such as GDP, unemployment, consumption, investment, the price level, and interest rates are used for governments to guide monetary and fiscal policy. Private firms use them for strategic planning, because economy-wide economic fluctuations typically have industry-level and firm-level effects. Financial speculation: Speculators in asset markets have an interest in forecasting asset returns (stock returns, interest rates, exchange rates, ...). Such forecasts are made routinely. 42 Forecasting in Econometrics • Financial risk management: Volatility forecasts are crucial for evaluating and insuring risks associated with asset portfolios. Volatility forecasts are also crucial for firms and investors who need to price assets such options and other derivatives. • We can distinguish two approaches: - Econometric (structural) forecasting - Time series forecasting • The distinction between the two types is somewhat blurred (e.g, VARs). 43 In-Sample Versus Out-of-Sample • Expect the “forecast” of the model to be good in-sample. • Say we have some data - e.g. monthly NYSE returns for 120 months: 1990M1 – 1999M12. We could use all of it to build the model, or keep some observations back: • A good test of the model since we have not used the information from 1999M1 onwards when we estimated the model parameters. 44 How to produce forecasts • • Multi-step ahead versus single-step ahead forecasts Recursive versus rolling windows • To understand how to construct forecasts, we need the idea of conditional expectations: E(yt+1 | Ωt ) • We cannot forecast a white noise process: E(ut+s | Ωt ) = 0 ∀ s > 0. • The two simplest forecasting “methods” 1. Assume no change : f(yt+s) = yt 2. Forecasts are the long term average f(yt+s) = 45 Models for Forecasting • Structural models e.g. y = Xβ + u yt = β1 + β 2 x2t + K + β k xkt + ut To forecast y, we require the conditional expectation...
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