Instability in regime switching models

In this paper, we look at the instability of a self-exciting regime-switching autoregressive model, specifically regime-switching models that are locally stable in each of their regimes. It turns out that the local stability of each regime is insufficient to ensure the overall stability of the model. The instability’s mechanism is described, and a sufficient condition for the instability is provided.

Transition from the Taylor rule to the zero lower bound

This paper examines the Taylor rule in the context of United States monetary policy since 1965, particularly with respect to the zero-lower-bound era of the federal funds rate from 2009 to 2016. A nonlinear Taylor rule is developed which features smooth transitions in the first two moments of the federal funds rate. This flexible specification is found to usefully capture observed nonlinearity, while accounting for the well-documented structural changes in monetary policy formation at the Federal Reserve in the last 50 years, and especially in the recent zero-lower-bound era.

A family of nonparametric unit root tests for processes driven by infinite variance innovations

This paper presents extensions to the family of nonparametric fractional variance ratio (FVR) unit root tests of Nielsen (2009. “A Powerful Test of the Autoregressive Unit Root Hypothesis Based on a Tuning Parameter Free Statistic.” Econometric Theory 25: 1515–44) under heavy tailed (infinite variance) innovations. In this regard, we first develop the asymptotic theory for these FVR tests under this setup. We show that the limiting distributions of the tests are free of serial correlation nuisance parameters, but depend on the tail index of the infinite variance process. Then, we compare the finite sample size and power performance of our FVR unit root tests with the well-known parametric ADF test under the impact of the heavy tailed shocks. Simulations demonstrate that under heavy tailed innovations, the nonparametric FVR tests have desirable size and power properties.

Recovering cointegration via wavelets in the presence of non-linear patterns

Johansen’s Cointegration Test (JCT) performs remarkably well in finding stable bivariate cointegration relationships. Nonetheless, the JCT is not necessarily designed to detect such relationships in presence of non-linear patterns such as structural breaks or cycles that fall in the low frequency portion of the spectrum. Seasonal adjustment procedures might not detect such non-linear patterns, and thus, we expose the difficulty in identifying cointegrating relations under the traditional use of JCT. Within several Monte Carlo experiments, we show that wavelets can empower more the JCT framework than the traditional seasonal adjustment methodologies, allowing for identification of hidden cointegrating relationships. Moreover, we confirm these results using seasonally adjusted time series as US consumption and income, gross national product (GNP) and money supply M1 and GNP and M2.

Prediction of stock index of two-scale long short-term memory model based on multiscale nonlinear integration

Although the prediction of stock prices and analyses of their returns and risks have always played integral roles in the stock market, accurate predictions are notoriously difficult to make, and mistakes may be devastatingly costly. This study attempts to resolve this difficulty by proposing and applying a two-stage long short-term memory (LSTM) model based on multi-scale nonlinear integration that considers a diverse array of factors. Initially, variational mode decomposition (VMD) is used to decompose an employed stock index to identify the different characteristics of the stock index sequence. Then, an LSTM model based on the multi-factor nonlinear integration of overnight information is established in a second stage. Finally, the joint VMD-LSTM model is used to predict the stock index. To validate the model, the Shanghai Composite, Nikkei 225, and Hong Kong Hang Seng indices were analyzed. Experiments show that, by comparison, the prediction effect of the mixed model is better than that of a single LSTM. For example, RMSE, MAE and MAPE of the mixed model of the Shanghai Composite Index are 4.22, 4.25 and 0.2 lower than the single model respectively. The RMSE, MAE and MAPE of the mixed model of the Nikkei 225 Index are 47.74, 37.21 and 0.17 lower than the single model respectively, and the RMSE, MAE and MAPE of the mixed model of the Hong Kong Hang Seng Index are 37.88, 25.06 and 0.08 lower than the single model respectively.

Consumption, aggregate wealth and expected stock returns: a quantile cointegration approach

This paper empirically examines the long-run relationship between consumption, asset wealth and labor income (i.e., cay) in the United States through the lens of a quantile cointegration approach. The advantage of using this approach is that it allows for a nonlinear relationship between these variables depending on the level of consumption. We estimate the coefficients using a Phillips–Hansen type fully modified quantile estimator to correct for the presence of endogeneity in the cointegrating relationship. To test for the null of cointegration at each quantile, we apply a quantile CUSUM test. Results show that: (i) consumption is more sensitive to changes in labor income than to changes in asset wealth for the entire distribution of consumption, (ii) the elasticity of consumption with respect to labor income (asset wealth) is larger at the right (left) tail of the consumption distribution than at the left (right) tail, (iii) the series are cointegrated around the median, but not in the tails of the distribution of consumption, (iv) using the estimated cay obtained for the right (left) tail of the distribution of consumption improves the long-run (short-run) forecast ability on real excess stock returns over a risk-free rate.

Forecasting transaction counts with integer-valued GARCH models

Using numerous transaction data on the number of stock trades, we conduct a forecasting exercise with INGARCH models, governed by various conditional distributions; the Poisson, the linear and quadratic negative binomial, the double Poisson and the generalized Poisson. The model parameters are estimated with efficient Markov Chain Monte Carlo methods, while forecast evaluation is done by calculating point and density forecasts.

What does Google say about credit developments in Brazil?

In this paper multivariate State Space (SS) models are used to evaluate and forecast household loans in Brazil, taking into account two Google search terms in order to identify credit demand: financiamento (type of loan used to finance goods) and empréstimo (a more general type of loan). Our framework is coupled with nonlinear features, such as Markov-switching and threshold point. We explore these nonlinearities to build identification strategies to disentangle the supply and demand forces which drive the credit market to equilibrium over time. We also show that the underlying nonlinearities significantly improves the performance of SS models on forecasting the household loans in Brazil, particularly in short-term horizons.