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on Econometric Time Series |
| By: | Cheng Yu; Dong Li; Feiyu Jiang; Ke Zhu |
| Abstract: | Matrix-variate time series data are largely available in applications. However, no attempt has been made to study their conditional heteroskedasticity that is often observed in economic and financial data. To address this gap, we propose a novel matrix generalized autoregressive conditional heteroskedasticity (GARCH) model to capture the dynamics of conditional row and column covariance matrices of matrix time series. The key innovation of the matrix GARCH model is the use of a univariate GARCH specification for the trace of conditional row or column covariance matrix, which allows for the identification of conditional row and column covariance matrices. Moreover, we introduce a quasi maximum likelihood estimator (QMLE) for model estimation and develop a portmanteau test for model diagnostic checking. Simulation studies are conducted to assess the finite-sample performance of the QMLE and portmanteau test. To handle large dimensional matrix time series, we also propose a matrix factor GARCH model. Finally, we demonstrate the superiority of the matrix GARCH and matrix factor GARCH models over existing multivariate GARCH-type models in volatility forecasting and portfolio allocations using three applications on credit default swap prices, global stock sector indices, and future prices. |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2306.05169&r=ets |
| By: | Markus Leippold (University of Zurich; Swiss Finance Institute); Hanlin Yang (University of Zurich) |
| Abstract: | We explore the performance of mixed-frequency predictive regressions for stock returns from the perspective of a Bayesian investor. We develop a constrained parameter learning approach for sequential estimation allowing for belief revisions. Empirically, we find that mixed-frequency models improve predictability, not only because of the combination of predictors with different frequencies but also due to the preservation of high-frequency features such as time-varying volatility. Temporally aggregated models misspecify the evolution frequency of the volatility dynamics, resulting in poor volatility timing and worse portfolio performance than the mixed-frequency specification. These results highlight the importance of preserving the potential mixed-frequency nature of predictors and volatility in predictive regressions. |
| Keywords: | Mixed-frequency data, predictive regressions, stochastic volatility, consumption-wealth ratio, parameter learning, portfolio optimization |
| JEL: | C11 C32 C53 G11 |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp2339&r=ets |
| By: | Kasper Johansson; Mehmet Giray Ogut; Markus Pelger; Thomas Schmelzer; Stephen Boyd |
| Abstract: | We consider the well-studied problem of predicting the time-varying covariance matrix of a vector of financial returns. Popular methods range from simple predictors like rolling window or exponentially weighted moving average (EWMA) to more sophisticated predictors such as generalized autoregressive conditional heteroscedastic (GARCH) type methods. Building on a specific covariance estimator suggested by Engle in 2002, we propose a relatively simple extension that requires little or no tuning or fitting, is interpretable, and produces results at least as good as MGARCH, a popular extension of GARCH that handles multiple assets. To evaluate predictors we introduce a novel approach, evaluating the regret of the log-likelihood over a time period such as a quarter. This metric allows us to see not only how well a covariance predictor does over all, but also how quickly it reacts to changes in market conditions. Our simple predictor outperforms MGARCH in terms of regret. We also test covariance predictors on downstream applications such as portfolio optimization methods that depend on the covariance matrix. For these applications our simple covariance predictor and MGARCH perform similarly. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.19484&r=ets |
| By: | Alex Maynard; Katsumi Shimotsu; Nina Kuriyama |
| Abstract: | This paper studies inference in predictive quantile regressions when the predictive regressor has a near-unit root. We derive asymptotic distributions for the quantile regression estimator and its heteroskedasticity and autocorrelation consistent (HAC) t-statistic in terms of functionals of Ornstein-Uhlenbeck processes. We then propose a switching-fully modified (FM) predictive test for quantile predictability with persistent regressors. The proposed test employs an FM style correction with a Bonferroni bound for the local-to-unity parameter when the predictor has a near unit root. It switches to a standard predictive quantile regression test with a slightly conservative critical value when the largest root of the predictor lies in the stationary range. Simulations indicate that the test has reliable size in small samples and particularly good power when the predictor is persistent and endogenous, i.e., when the predictive regression problem is most acute. We employ this new methodology to test the ability of three commonly employed, highly persistent and endogenous lagged valuation regressors - the dividend price ratio, earnings price ratio, and book to market ratio - to predict the median, shoulders, and tails of the stock return distribution. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2306.00296&r=ets |
| By: | Jad Beyhum; Jonas Striaukas |
| Abstract: | GDP nowcasting commonly employs either sparse regression or a dense approach based on factor models, which differ in the way they extract information from high-dimensional datasets. This paper aims to investigate whether augmenting sparse regression with (estimated) factors can improve nowcasts. We propose an estimator for a factor-augmented sparse MIDAS regression model. The rates of convergence of the estimator are derived in a time series context, accounting for $\tau$-mixing processes and fat-tailed distributions. The application of this new technique to nowcast US GDP growth reveals several key findings. Firstly, our novel technique significantly improves the quality of nowcasts compared to both sparse regression and plain factor-augmented regression benchmarks over a period period from 2008 Q1 to 2022 Q2. This improvement is particularly pronounced during the COVID pandemic, indicating the model's ability to capture the specific dynamics introduced by the pandemic. Interestingly, our novel factor-augmented sparse method does not perform significantly better than sparse regression prior to the onset of the pandemic, suggesting that using only a few predictors is sufficient for nowcasting in more stable economic times. |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2306.13362&r=ets |
| By: | Bjoern Schulte-Tillmann; Mawuli Segnon; Timo Wiedemann |
| Abstract: | We study the accuracy of a variety of parametric price duration-based realized variance estimators constructed via various financial duration models and compare their forecasting performance with the performance of various non-parametric return-based realized variance estimators. Our financial duration models consist of an ACD(1, 1), its logarithmic version, Log-ACD(1, 1), and its long-memory version, FIACD(1, 1), as well as the Markov-switching multifractal duration (MSMD) model and the factorial hidden Markov duration (FHMD) process. In an empirical study using highfrequency data on ten stocks traded on the New York stock exchange (NYSE) our in- and out-of-sample results show that the parametric price duration-based realized variance (RV) estimators, especially the ACD-based RV estimator, seem to be robust to price jumps and microstructure noise and perform better than the non-parametric return-based RV estimators. Furthermore, we also find that the price duration-based and return-based RV models perform relatively well and produce more accurate and valid value-at-risk forecasts than the GARCH(1, 1). |
| Keywords: | Price duration; Realized variance estimator; Value-at-risk; High frequency data |
| JEL: | C41 C52 C53 |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:cqe:wpaper:10523&r=ets |
| By: | Vygintas Gontis |
| Abstract: | Identifying the best possible models based on given empirical data of observed time series is challenging. The financial markets provide us with vast empirical data, but the best model selection is still problematic for researchers. The widely used long-range memory and self-similarity estimators give varying values of the parameters as these estimators are developed for specific time series models. Previously we investigated the order disbalance time series from the general fractional L\'{e}vy stable motion perspective and discovered the stable anti-correlation in the order flow of financial markets. Nevertheless, a more detailed consideration of empirical data suggests we construct a more specific order flow model based on the power-law distribution of limit order cancellation times. In the event time consideration, the limit order cancellation times follow the discrete probability mass function derived from the Tsallis q-Exponential distribution. The power-law distribution of the limit order volumes and power-law cancellation times form the new approach to modeling order disbalance in the financial markets. Proposed modeling can be an example of opinion dynamics in social systems. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2306.00093&r=ets |
| By: | Espasa, Antoni; Carlomagno Real, Guillermo |
| Abstract: | The paper starts commenting on the hard tasks of data treatment -mainly, cleaning, classification, and aggregation- that are required at the beginning of any analysis with big data. Subsequently, it focuses on non-financial big data time series of high frequency that for many problems are aggregated at daily, hourly, or higher frequency levels of several minutes. Then, the paper discusses possible stylized facts present in these data. In this respect, it studies relevant seasonality: daily, weekly, monthly, and annually, and analyses how, for the data in question, these cycles could be affected by weather variables and by factors due to the annual composition of the calendar. Consequently, the paper investigates the possible main characteristics of the mentioned cycles and the types of responses to the exogenous weather and calendar factors that data could show. The shorter cycles could change along the annual cycle and interact with the exogenous variables. The modelling strategy could require regime-switching, dynamic, non-linear structures, and interactions between the factors considered. Then the paper analyses the construction of explanatory variables that could be useful for taking into account all the above peculiarities. We propose the use of the automated procedure, Autometrics, to discover -in words of Prof Hendry- a parsimonious model not dominated by any other, which is able to explain all the characteristics of the data. The model can be used for structural analysis, forecasting, and, when it is the case, to build real-time quantitative macroeconomic leading indicators. Finally, the paper includes an application to the daily series of jobless claims in Chile. |
| Keywords: | Aggregation; Several Seasonality (Daily, Weekly, Monthly And Annual); Complex Annual Calendar Composition; Weather Variables; Interactive Effects; Switching Regimes; Multiplicative; Dynamic and Non-Linear Structures; Designing of Exogenous Variables; Autometrics; Macroeconomic Leading Indicators; Jobless Claims |
| JEL: | C01 C22 C55 |
| Date: | 2023–07–04 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:37746&r=ets |
| By: | Runyu Dai; Yasumasa Matsuda |
| Abstract: | In this paper, we propose a parsimonious model to estimate large volatility matrices by combining DCC-GARCH, sparsity-induced weak factors (sWFs) and POET framework in Fan et al. (2013). We call this method the DCC and sWFs extended POET (DCC-ePOET). Built on the mixed factor structures, we estimate volatility matrices through the univariate volatilities of observable factors and weak latent factors with a linear transformation. We further include a sparse noise covariance estimator obtained by an aptivethreshold method proposed in POET to dressthe singularity issue when the cross-sectional dimension N is larger than the sample size T, and capture the weak correlations in the factor models'idiosyncratic terms. Simulation studies show that our proposed method achieves good finite-sample performance. Empirical studies demonstrate that the developed method is superior to several candidates in the analysis of out-of-sample minimum variance portfolio allocations. |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:toh:dssraa:135&r=ets |