Evidence Of Nonlinear Mean Reversion Research Articles

London calling: Nonlinear mean reversion across national stock markets

This paper revisits empirical evidence of mean reversion of relative stock prices in international stock markets. We implement a strand of univariate and panel unit root tests for linear and nonlinear models of 18 national stock indices from 1969 to 2016. Our major findings are as follows. First, we find strong evidence of nonlinear mean reversion of the relative stock price with the UK index as the reference, calling attention to the stock index in the UK, but not with the US index. Our results imply an important role of the local common factor in the European stock markets. Second, panel tests yield no evidence of linear and nonlinear stationarity when the cross-section dependence is considered, which provides conflicting results from those of the univariate tests. Last, we show how to understand these results via dynamic factor analysis. When the stationary common factor dominates nonstationary idiosyncratic components in small samples, panel tests that filter out the stationary common factor may yield evidence against the stationarity null hypothesis in finite samples. We corroborate this conjecture via extensive Monte Carlo simulations.

Nonlinear integration of London and Amsterdam stock markets in the 1700s

The financial markets in London and Amsterdam were some of the first to develop. Using threshold autoregressive models, we use data on two commonly traded stocks in these cities to show that the joint behaviour of the prices is consistent with the theory of arbitrage in the presence of transportation costs. The results suggest that prices converged more quickly as the price difference between the two markets increased. We also show that the threshold estimates are consistent between assets and across time. These results provide some of the earliest evidence of nonlinear mean reversion in asset prices in geographically separate financial markets.

Evidence of nonlinear mean reversion in the real interest rate

This article utilizes tests for a unit root that have power against nonlinear alternatives to provide empirical evidence on the time series properties of the ex-post real interest rate in the G7 countries. We find that the unit root hypothesis can be rejected in the presence of a nonlinear alternative motivated by theoretical literature on optimal monetary policy rules. This represents a reversal of the results obtained using standard linear unit-root and cointegration tests. Tests for linearity reject this hypothesis for Canada, France, Italy and Japan for which we estimate nonlinear models capturing the dynamics of the interest rate. For these countries, ex-post real interest rates follow a nonlinear model characterized by mean reversion and provide statistical evidence for the Fisher effect.

PPP: Delusion or Reality? Evidence from a Nonlinear Analysis

In this paper we analyze the validity of the purchasing power parity (PPP) in a nonlinear framework using data for 18 bilateral US dollar exchange rates. Following Enders and Ludlow (2002), we use unit root and cointegration tests that do not assume a specific nonlinear adjustment. We find evidence of non-linear mean reversion in deviations from the PPP equilibrium in 11 out of 18 currencies. Additionally, to disentangle the respective contribution of exchange rate and prices to the adjustment toward the long run equilibrium, we estimate a Vector Error Correction Model. According to our empirical analysis, there exists a nonlinear mechanism to correct for deviation from the PPP equilibrium that comes mainly from the exchange rates. This is consistent with theoretical arguments on international goods markets under transaction costs as well as with an emerging strand of empirical literature. These results highlight the importance of neglecting the possibility of nonlinearity in the debate about the PPP and provide empirical evidence that supports the scenario of the PPP hypothesis as a reality.

Nonlinear mean reversion in the G7 stock markets

We utilize the nonlinear unit root tests proposed by Park and Shintani (2005) and find strong evidence of nonlinear mean reversion between a US stock index and the stock indices in France, Germany, Italy and the UK. We identified an inaction band where deviations of these international stock indices from the US stock index follow a unit root process. Outside the band, however, they exhibit strong mean reversion properties. We show that standard linear unit root tests are not able to detect nonlinear cointegration and will yield the erroneous conclusion that the stock indices are not cointegrated.

Threshold Adjustment of Deviations from the Law of One Price

Using self-exciting threshold autoregressive models, we explore the validity of the law of one price (LOOP) for sixteen sectors in nine European countries. We find strong evidence of nonlinear mean reversion in deviations from the LOOP and highlight the importance of modelling the real exchange rate in a nonlinear fashion in an attempt to measure speeds of real exchange rate adjustment. Using the US dollar as a reference currency, the half-lives of sectoral real exchange rate shocks, calculated by Monte Carlo integration, imply much faster adjustment than the 'consensus' half-life estimates of three to five years. The results also imply that transaction costs vary significantly across sectors and countries.

Threshold Adjustment in Deviations from the Law of One Price

Using self-exciting threshold autoregressive models, we explore the validity of the law of one price (LOOP) for sixteen sectors in nine European countries. We and strong evidence of nonlinear mean reversion in deviations from the LOOP and highlight the importance of modelling the real exchange rate in a nonlinear fashion in an attempt to measure speeds of real exchange rate adjustment. Using the US dollar as a reference currency, the half-lives of sectoral real exchange rates shocks, calculated by Monte Carlo integration, imply much faster adjustment than the consensus half-life estimates of three to five years. The results also imply that transaction costs vary significantly across sectors and countries.

Further on nonlinearity, persistence, and integration properties of real exchange rates

Integration, nonlinearity, and persistence dynamics of several quarterly US-Dollar-denominated real exchange rates are investigated by using new unit root tests, simulated p-values for linearity tests, estimation of smooth transition autoregressive (STAR) models, and simulation of autocorrelation functions. This paper uses a simulation-based approach to study covariance stationarity and persistence dynamics of the estimated models. Findings in the paper provide evidence of nonlinear mean reversion for several series albeit with some persistence. Results also reveal considerable variation in the degree of persistence and timing of switches across extreme regimes in ESTAR models between Euro and non-Euro area currencies.

Are there nonlinearities in short-term interest rates?

The present paper investigates the characteristics of short-term interest rates in several countries. We examine the importance of nonlinearities in the mean reversion and volatility of short-term interest rates. We examine various models that allow the conditional mean (drift) and conditional variance (diffusion) to be functions of the current short rate.We find that different markets require different models. In particular, we find evidence of nonlinear mean reversion in some of the countries that we examine, linear mean reversion in others and no mean reversion in some countries. For all countries we examine, there is strong evidence of the need for the volatility of interest rate changes to be highly sensitive to the level of the short-term interest rate. Out-of-sample forecasting performance of one-factor short rate models is poor, stemming from the inability of the models to accommodate jumps and discontinuities in the time series data.

Nonlinear dynamics in deviations from the law of one price: a broad-based empirical study

In this paper we test empirically the validity of the law of one price using data for five major bilateral US dollar exchange rates and nine goods sectors during the recent floating exchange rate regime since the early 1970s. Using threshold autoregressive models, we find strong evidence of nonlinear mean reversion in deviations from the law of one price with plausible convergence speeds. Consistent with theoretical arguments on international goods markets arbitrage under transactions costs and with an emerging strand of empirical literature, these results contribute towards forming a consensus view in favor of discrete regime switching in deviations from the law of one price and the presence of differing nonzero transactions costs across a broad range of goods and countries.

The behavior of US public debt: a nonlinear perspective

This letter provides strong evidence of nonlinear mean reversion in the US debt-GDP ratio using data since 1916 and shows that the difficulty to detect mean reversion encountered by a number of researchers may be due to the invalid maintained hypothesis of linearity which is common to the testing procedures employed in this context.

Why is it so Difficult to Beat the Random Walk Rorecast of Exchange Rates?

We propose an exchange rate model that can explain both the observed volatility and the persistence of real and nominal exchange rate movements and thus in some measure resolves Rogoff's (1996) purchasing power parity puzzle. Our analysis reconciles the well-known difficulties in beating the random walk forecast model with the statistical evidence of nonlinear mean reversion in deviations from fundamentals. Our analysis also provides a compelling rationale for the long-horizon predictability of exchange rates. We find strong empirical support for long-horizon predictability, and we explain why it is difficult to exploit this predictability in real-time forecasts. Our results not only lend support to economists' beliefs that the exchange rate is inherently predictable, but they also help us to understand the reluctance of applied forecasters to abandon chartist methods in favor of models based on economic fundamentals.