New in-sample prediction errors in time series with applications

^aThis article introduces two new types of prediction errors in time series: the filtered prediction errors and the deletion prediction errors. These two prediction errors are obtained in the same sample used for estimation, but in such a way that they share some common properties with out of sample prediction errors. It is proved that the filtered prediction errors are uncorrelated, up to terms of magnitude order O(T^-2), with the in sample innovations, a property that share with the out-of-sample prediction errors. On the other hand, deletion prediction errors assume that the values to be predicted are unobserved, a property that they also share with out-of-sample prediction errors. It is shown that these prediction errors can be computed with parameters estimated by assuming innovative or additive outliers, respectively, at the points to be predicted. Then the prediction errors are obtained by running the procedure for all the points in the sample of data. Two applications of these new prediction errors are presented. The first is the estimation and comparison of the prediction mean squared errors of competing predictors. The second is the determination of the order of an ARMA model. In the two applications the proposed filtered prediction errors have some advantages over alternative existing methods.

PROPERTIES OF PREDICTORS IN OVERDIFFERENCED NEARLY NONSTATIONARY AUTOREGRESSION

This paper analyzes the effect of overdifferencing a stationary AR(p+1) process whoselargest root is near unity. It is found that if the process is nearly nonstationary, the estimators ofthe overdifferenced model ARIMA (p, 1, 0) are root-T consistent. It is also found that thismisspecified ARIMA (p, 1, 0) has lower predictive mean squared error, to terms of small order,that the properly specified AR(p+1) model due to its parsimony. The advantage of theoverdifferenced predictor depends on the remaining roots, the prediction horizon, and the meanof the process.Autoregressive processes, near nonstationarity, overdifferencing

NEW IN-SAMPLE PREDICTION ERRORS IN TIME SERIES WITH APPLICATIONS

This article introduces two new types of prediction errors in time series: the filtered prediction errors and the deletion prediction errors. These two prediction errors are obtained in the same sample used for estimation, but in such a way that they share some common properties with out of sample prediction errors. It is proved that the filtered prediction errors are uncorrelated, up to terms of magnitude order O(T-2), with the in sample innovations, a property that share with the out-of-sample prediction errors. On the other hand, deletion prediction errors assume that the values to be predicted are unobserved, a property that they also share with out-of-sample prediction errors. It is shown that these prediction errors can be computed with parameters estimated by assuming innovative or additive outliers, respectively, at the points to be predicted. Then the prediction errors are obtained by running the procedure for all the points in the sample of data. Two applications of these new prediction errors are presented. The first is the estimation and comparison of the prediction mean squared errors of competing predictors. The second is the determination of the order of an ARMA model. In the two applications the proposed filtered prediction errors have some advantages over alternative existing methods..

Debt refinancing and credit risk

Many firms choose to refinance their debt. We investigate the long run effects of this extended practice on credit ratings and credit spreads. We find that debt refinancing generates systematic rating downgrades unless a minimum firm value growth is observed. Deviations from this growth path imply asymmetric results: A lower value growth generates downgrades and a higher value growth upgrades as expected. However, downgrades will tend to be higher in absolute terms. On the other hand, credit spreads will be independent of the risk free interest rate in the short run, but positively correlated with this rate in the long run

Credit spreads: theory and evidence about the information content of stocks, bonds and cdss

This paper presents a procedure for computing homogeneous measures of credit risk from stocks, bonds and CDSs. The measures are based on bond spreads (BS), CDS spreads (CDS) and implied stock market credit spreads (ICS). We compute these measures for a sample of North American and European firms and find that in most cases, the stock market leads the credit risk discovery process with respect to bond and CDS markets

Dimensionality reduction with image data

A common objective in image analysis is dimensionality reduction. The most common often used data-exploratory technique with this objective is principal component analysis. We propose a new method based on the projection of the images as matrices after a Procrustes rotation and show that it leads to a better reconstruction of images

A multivariate Kolmogorov-Smornov test of goodnes of fit

This paper presents a distribution free multivariate Kolmogorov-Smirnov goodıness of fit test. The test uses an statistic which is built using Rosenblatt's transformation and an algorithm is developed to compute it in the bivariate case. An approximate test, that can be easily computed in any dimension, is also presented. The power of these multivariate tests is studied in a simulationı study

Graphical identification of TAR models

This paper proposes an automatic procedure to identify Threshold Autoregressive models and specify the threshold values. The proposed procedure is based on recursive estimation of arranged autoregression. The main advantage of the proposed procedure over its competitors is that the threshold values are automatically detected. The performance of the proposed procedure is evaluated using simulations and real data.Nonlinear time series, Recursive estimation, Arranged autoregression, TAR models, Nonlinearity test