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A SingleBlind Controlled Competition Among Tests for Nonlinearity and Chaos; Further Results. Unpublished memo UIC Department of Economics
, 1998
"... Abstract: BarnettGallantHinichJungeilgesKaplanJensen (1997) conducted a blind study of the power of a number of nonlinearity tests. This note questions their findings for the Hinich (1982) test by reanalyzing the data for a range of bandwidths. In contrast to the original findings that were not ..."
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Abstract: BarnettGallantHinichJungeilgesKaplanJensen (1997) conducted a blind study of the power of a number of nonlinearity tests. This note questions their findings for the Hinich (1982) test by reanalyzing the data for a range of bandwidths. In contrast to the original findings that were not able to reject linearity for the GARCH, NLMA and ARCH models, our findings show that linearity is significantly rejected. The power of the original Hinich (1982) test and a proposed modification was examined using Monte Carlo methods.
FORECASTING THE SPOT PRICES OF VARIOUS COFFEE TYPES USING LINEAR AND NONLINEAR ERROR CORRECTION MODELS
"... This paper estimates linear and nonlinear error correction models for the spot prices of four different coffee types. In line with economic priors, we find some evidence that when prices are too high, they move back to equilibrium more slowly than when they are too low. This may reflect the fact th ..."
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This paper estimates linear and nonlinear error correction models for the spot prices of four different coffee types. In line with economic priors, we find some evidence that when prices are too high, they move back to equilibrium more slowly than when they are too low. This may reflect the fact that, in the short run, it is easier for countries to restrict the supply of coffee in order to raise prices, rather than increase supply in order to reduce them. Further, there is some evidence that adjustment is faster when deviations from the equilibrium level get larger. Our forecasting analysis suggests that asymmetric and nonlinear error correction models offer weak evidence of improved forecasting performance relative to the random walk model.
GARCH DIAGNOSIS WITH PORTMANTEAU BICORRELATION TEST AN APPLICATION ON THE MALAYSIA’S STOCK MARKET
"... This study employed the Hinich portmanteau bicorrelation test (Hinich and Patterson, 1995; Hinich, 1996) as a diagnostic tool to determine the adequacy of the GARCH model in describing the returns generating process of Malaysia’s stock market, specifically the Kuala Lumpur Stock Exchange Composite I ..."
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This study employed the Hinich portmanteau bicorrelation test (Hinich and Patterson, 1995; Hinich, 1996) as a diagnostic tool to determine the adequacy of the GARCH model in describing the returns generating process of Malaysia’s stock market, specifically the Kuala Lumpur Stock Exchange Composite Index (KLSE CI). The bicorrelation results demonstrated that, while GARCH model is commonly applied to financial time series, this model cannot provide an adequate characterization for the underlying process of KLSE CI. Further investigation using the windowed test procedure revealed that this was due to the presence of episodic nonstationarity in the data, which could not be captured by any kind of ARCH or GARCH model, even after modifications to the specifications of the GARCH model. Thus, this study points to the need to continue the search for a parsimonious and congruent model capable of capturing the episodic features presence in the returns series of KLSE CI. Keywords: GARCH; Nonlinearity; Nonstationarity; Data generating process; Bicorrelation; Malaysian stock market.
Bootstrap, Empirical size and power
"... We propose a new test based on a Fourier series to approximate the unknown form of a nonlinear timeseries model. The test has good size and power properties to detect structural breaks, seasonal parameters and random coefficients. Moreover, it has reasonable power to discriminate between nonlineari ..."
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We propose a new test based on a Fourier series to approximate the unknown form of a nonlinear timeseries model. The test has good size and power properties to detect structural breaks, seasonal parameters and random coefficients. Moreover, it has reasonable power to discriminate between nonlinearity in variables and nonlinearity in parameters. We use the test to show that U.S. inflation is appropriately estimated with a timevarying intercept that jumps in the late 1960’s, peaks in the early 1980’s and then begins to decline. German income and consumption data is used to illustrate the ability of the test to suggest the form of the nonlinearity. Keywords: Timevarying parameters, Fourierseries approximation, Nuisance parameters,
{Preliminary – please do not quote} IDENTIFICATION OF COEFFICIENTS IN A QUADRATIC MOVING AVERAGE PROCESS USING THE GENERALIZED METHOD OF MOMENTS
, 2002
"... The output of a causal, stable, timeinvariant nonlinear filter can be approximately represented by the linear and quadratic terms of a finite parameter Volterra series expansion. We call this representation the “quadratic nonlinear MA model ” since it is the logical extension of the usual linear MA ..."
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The output of a causal, stable, timeinvariant nonlinear filter can be approximately represented by the linear and quadratic terms of a finite parameter Volterra series expansion. We call this representation the “quadratic nonlinear MA model ” since it is the logical extension of the usual linear MA process. Where the actual generating mechanism for the data is fairly smooth, this quadratic MA model should provide a better approximation to the true dynamics than the twostate threshold autoregression and Markov switching models usually considered. As with linear MA processes, the nonlinear MA model coefficients can be estimated via least squares fitting, but it is essential to begin with a reasonably parsimonious model identification and nonarbitrary preliminary estimates for the parameters. In linear ARMA modeling these are derived from the sample correlogram and the sample partial correlogram, but these tools are confounded by nonlinearity in the generating mechanism. Here we obtain analytic expressions for the second and third order moments – the autocovariances and third order cumulants – of a quadratic MA process driven by i.i.d. symmetric innovations. These expressions allow us to identify the significant coefficients in the process by using GMM to obtain preliminary coefficient estimates and their concomitant estimated standard errors. The utility of the method for specifying nonlinear time series models is illustrated using artificially generated data. 1We focus here on parametric modeling methods because we are more sanguine as to the feasibility of applying such methods to macroeconomic and financial data sets in which the sample length has been restricted so as to make reasonably credible the assumption of a stable relationship. Granger and Teräsvirta (1993, Chapter 7) review alternative – nonparametric and semiparametric – approaches; they also review several parametric approaches – e.g., bilinear models – which cannot be classified as “switching regressions.”
Brief Title: Detecting Non Linearity
"... This article analyses the use of model selection criteria for detecting non linearity in the residuals of a linear model. Model selection criteria are applied for finding the order of the best autorregressive model fitted to the squared residuals of the linear model. If the order selected is not zer ..."
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This article analyses the use of model selection criteria for detecting non linearity in the residuals of a linear model. Model selection criteria are applied for finding the order of the best autorregressive model fitted to the squared residuals of the linear model. If the order selected is not zero, this is considered as an indication of non linear behavior. The BIC and AIC criteria are compared in three Monte Carlo experiments to some popular nonlinearity tests. We conclude that the BIC model selection criterion seems to offer a promising tool for detecting non linearity in time series. An example is shown to illustrate the performance of the tests considered and the relationship between non linearity and structural changes in time series.
Thoughts on Credit Risk Diversification: Comparing Credit Ratings Volatility Across Asset Classes
"... fundamental change is taking place in the fixed income markets— a change that is good for commercial mortgagebacked securities (CMBS). In the past, most investors had compartmentalized investment strategies. They focused on security selection within one or a narrow range of sectors. Investors now ..."
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fundamental change is taking place in the fixed income markets— a change that is good for commercial mortgagebacked securities (CMBS). In the past, most investors had compartmentalized investment strategies. They focused on security selection within one or a narrow range of sectors. Investors now increasingly base decisions on the risk/reward tradeoffs across sectors. On the surface, it might appear that this change was sparked by the collapse of Enron. We certainly did see a major redirection of funds away from stocks and corporate bonds and into the relative safety of structured finance after the Enron story broke, and this trend has only grown as each successive corporate scandal (Adelphia, WorldCom, Xerox, Vivendi Universal, etc.) reinforces the fear that the corporate world has widespread accounting problems. But in fact, the move to invest across markets has been underway for some time now, driven by consolidation on the buy side. As more and more money rests in fewer and fewer hands, the logic of investing broadly across markets has become more than compelling — it has become unavoidable. The Enron collapse simply added fuel (actually, a lot of fuel) to an existing fire. It encouraged a system already capable of moving money across markets to reevaluate the risk/reward tradeoffs of corporates versus structured finance. The conclusion, reached by firm after firm, is that structured finance products in general, and CMBS in particular, look a lot better than corporate bonds. While this change is good for the CMBS market, in that it brings more sponsorship to CMBS, it also exposes traditional corporate investors to new types of risk that they may not fully understand. A good way to evaluate the credit risks across asset classes is to use ratings probability transition matrices.
1 Episodic Nonlinearity in Eastern European Stock Market Indices
"... In this paper we check for nonlinear behavior of the nine most important Eastern European stock market indices. Using a battery of five nonlinear test: the Hinich bicorrelation (jointly with the windowed testing procedure), the BDS, the Engle LM, the McLeodLi and the Tsay tests we find systematic n ..."
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In this paper we check for nonlinear behavior of the nine most important Eastern European stock market indices. Using a battery of five nonlinear test: the Hinich bicorrelation (jointly with the windowed testing procedure), the BDS, the Engle LM, the McLeodLi and the Tsay tests we find systematic nonlinear structure in the rate of return series. Our results suggest that for most of these series the nonlinear serial dependencies are episodic in nature. We identify the period of time where the nonlinearity is stronger. All the stock market returns (with the exception of Poland) present some form of nonlinearity. Our findings support the idea that, in these transitions stock market the weakform of the efficient market hypothesis can not be supported.