Asymptotically Optimal Smoothing with ARCH Models / Daniel B. Nelson.

By:

Nelson, Daniel B

Contributor(s):

National Bureau of Economic Research

Material type: Text

TextSeries: Technical Working Paper Series (National Bureau of Economic Research) ; no. t0161.Publication details: Cambridge, Mass. National Bureau of Economic Research 1994.Description: 1 online resource: illustrations (black and white)Subject(s):

C32 - Time-Series Models • Dynamic Quantile Regressions • Dynamic Treatment Effect Models • Diffusion Processes • State Space Models

Online resources:

Available additional physical forms:

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Abstract: Suppose an observed time series is generated by a stochastic volatility model-i.e., there is an unobservable state variable controlling the volatility of the innovations in the series. As shown by Nelson (1992), and Nelson and Foster (1994), a misspecified ARCH model will often be able to consistently (as a continuous time limit is approached) estimate the unobserved volatility process, using information in the lagged residuals. This paper shows how to more efficiently estimate such a volatility process using information in both lagged and led residuals. In particular, this paper expands the optimal filtering results of Nelson and Foster (1994) and Nelson (1994) to smoothing.

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Previous	nber t0158 Biases in Twin Estimates of the Return to Schooling: A Note on Recent Research /	nber t0159 Interpreting Tests of the Convergence Hypothesis /	nber t0160 Reported Income in the NLSY: Consistency Checks and Methods for Cleaningthe Data /	nber t0161 Asymptotically Optimal Smoothing with ARCH Models /	nber t0162 Asymptotic Filtering Theory for Multivariate ARCH Models /	nber t0163 Continuous Record Asymptotics for Rolling Sample Variance Estimators /	nber t0164 Evidence on Structural Instability in Macroeconomic Time Series Relations /	Next

August 1994.

Suppose an observed time series is generated by a stochastic volatility model-i.e., there is an unobservable state variable controlling the volatility of the innovations in the series. As shown by Nelson (1992), and Nelson and Foster (1994), a misspecified ARCH model will often be able to consistently (as a continuous time limit is approached) estimate the unobserved volatility process, using information in the lagged residuals. This paper shows how to more efficiently estimate such a volatility process using information in both lagged and led residuals. In particular, this paper expands the optimal filtering results of Nelson and Foster (1994) and Nelson (1994) to smoothing.