Mixed-frequency Models Research Articles

Modelling Mixed-Frequency Time Series with Structural Change

AbstractPredictive ability of time series models is easily compromised in the presence of structural breaks, common among financial and economic variables amidst market shocks and policy regime shifts. We address this problem by estimating a semiparametric mixed-frequency model, that incorporate high frequency data either in the conditional mean or the conditional variance equation. The inclusion of high frequency data through non-parametric smoothing functions complements the low frequency data to capture possible non-linear relationships triggered by the structural change. Simulation studies indicate that in the presence of structural change, the varying frequency in the mean model provides improved in-sample fit and superior out-of-sample predictive ability relative to low frequency time series models. These hold across a broad range of simulation settings, such as varying time series lengths, nature of structural break points, and temporal dependencies. We illustrate the relative advantage of the method in predicting stock returns and foreign exchange rates in the case of the Philippines.

Improved Breitung and Roling estimator for mixed-frequency models with application to forecasting inflation rates

Instead of applying the commonly used parametric Almon or Beta lag distribution of MIDAS, Breitung and Roling (J Forecast 34:588–603, 2015) suggested a nonparametric smoothed least-squares shrinkage estimator (henceforth SLS1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${SLS}_{1}$$\\end{document}) for estimating mixed-frequency models. This SLS1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${SLS}_{1}$$\\end{document} approach ensures a flexible smooth trending lag distribution. However, even if the biasing parameter in SLS1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${SLS}_{1}$$\\end{document} solves the overparameterization problem, the cost is a decreased goodness-of-fit. Therefore, we suggest a modification of this shrinkage regression into a two-parameter smoothed least-squares estimator (SLS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${SLS}_{2}$$\\end{document}). This estimator solves the overparameterization problem, and it has superior properties since it ensures that the orthogonality assumption between residuals and the predicted dependent variable holds, which leads to an increased goodness-of-fit. Our theoretical comparisons, supported by simulations, demonstrate that the increase in goodness-of-fit of the proposed two-parameter estimator also leads to a decrease in the mean square error of SLS2,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${SLS}_{2},$$\\end{document} compared to that of SLS1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${SLS}_{1}$$\\end{document}. Empirical results, where the inflation rate is forecasted based on the oil returns, demonstrate that our proposed SLS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${SLS}_{2}$$\\end{document} estimator for mixed-frequency models provides better estimates in terms of decreased MSE and improved R2, which in turn leads to better forecasts.

Does energy consumption play a key role? Re-evaluating the energy consumption-economic growth nexus from GDP growth rates forecasting

Given the strong link between economic growth and energy consumption, we construct a new set of energy consumption indices (ECI) to forecast GDP growth rates. The findings demonstrate the strong predictive power of the new indices. In particular, the electricity consumption index from the industrial sector has an excellent predictive performance and deserves the attention of the government and academia to help formulate economic growth targets. The mixed-frequency model with the Least Absolute Shrinkage and Selection Operator approach (MIDAS-LASSO) enables the full exploitation of energy consumption information for stable forecasting performance, even in the context of crisis fluctuations and geopolitical risk shocks. Furthermore, we apply forecast encompassing tests and variable selection to statistically investigate the predictive information. By analyzing energy consumption characteristics, we contribute to the economic growth hypothesis at the level of energy consuming sectors and provide new insights into GDP forecasting.

Stock market volatility and economic policy uncertainty: New insight into a dynamic threshold mixed-frequency model

This study re-examines the relationship between U.S. stock market volatility and economic policy uncertainty (EPU) using the mixed-frequency dynamic threshold model. The empirical results exhibit several findings. The EPU has a threshold effect that is time-varying. Moreover, combining the dynamic threshold with the Markov-regime Mix-frequency model (MS-MIDAS), we find that this new model can significantly improve the predictive performance in a statistical view compared to other competing models (including the benchmark model). Our findings can provide new insight into volatility forecasting.

Tourism Demand Forecasting With Multiple Mixed-Frequency Data: A Reverse Mixed-Data Sampling Method

Due to the limitations of existing tourism demand forecasting models, data with frequencies lower than those of the tourism demand need to be processed in advance and cannot be directly used in a model, which leads to the loss of timeliness and accuracy in tourism demand forecasting. Taking the inbound tourism of the United States prior to and during the COVID-19 pandemic as an example, this study systematically examines the impact of data frequency processing on tourism demand modeling and forecasting, through the construction and comparison of three categories of models, with a particular focus on the first developed multiple mixed-frequency specification of reverse mixed-data sampling (RMIDAS) model. The results confirm the positive effect of multiple mixed-frequency models, which can directly use various original data frequencies, in improving the accuracy of tourism demand forecasting. This study also provides important guidance for future research on high-frequency tourism variables forecasting.

Effectiveness of Principal-Component-Based Mixed-Frequency Error Correction Model in Predicting Gross Domestic Product

As an important indicator that can reflect a country’s macroeconomic situation and future trend, experts and scholars have long focused on analyses and predictions of gross domestic product (GDP). Combining principal component analysis (PCA), the mixed-frequency data sampling (MIDAS) model and the error correction model (ECM), this investigation constructs the principal-component-based ECM-MIDAS and co-integration MIDAS (CoMIDAS) models, respectively. After that, this investigation uses the monthly consumption, investment and trade data to build a mixed-frequency model to predict quarterly GDP. The empirical results can be summarized as follows: First, the predictive effectiveness of the mixed-frequency model is better than that of the same-frequency model. Second, the three variables have a strong correlation, and applying the principal component idea when modelling the same and mixed frequencies can lead to more favourable predictive effectiveness. Third, adding an error correction term to the principal-component-based mixed-frequency model has a significant coefficient and a higher predictive accuracy. Based on the above, it can be concluded that combining the MIDAS model with error correction and a principal component is effective; thus, this combination may be applied to support real-time and accurate macroeconomic prediction.

Total Electricity Consumption Forecasting Based on Temperature Composite Index and Mixed-Frequency Models

ABSTRACT The total electricity consumption (TEC) can accurately reflect the operation of the national economy, and the forecasting of the TEC can help predict the economic development trend, as well as provide insights for the formulation of macro policies. Nowadays, high-frequency and massive multi-source data provide a new way to predict the TEC. In this paper, a “seasonal-cumulative temperature index” is constructed based on high-frequency temperature data, and a mixed-frequency prediction model based on multi-source big data (Mixed Data Sampling with Monthly Temperature and Daily Temperature index, MIDAS-MT-DT) is proposed. Experimental results show that the MIDAS-MT-DT model achieves higher prediction accuracy, and the “seasonal-cumulative temperature index” can improve prediction accuracy.

From Quarterly to Monthly Turnover Figures Using Nowcasting Methods

Abstract Short-term business statistics at Statistics Netherlands are largely based on Value Added Tax (VAT) administrations. Companies may decide to file their tax return on a monthly, quarterly, or annual basis. Most companies file their tax return quarterly. So far, these VAT based short-term business statistics are published with a quarterly frequency as well. In this article we compare different methods to compile monthly figures, even though a major part of these data is observed quarterly. The methods considered to produce a monthly indicator must address two issues. The first issue is to combine a high- and low-frequency series into a single high-frequency series, while both series measure the same phenomenon of the target population. The appropriate method that is designed for this purpose is usually referred to as “benchmarking”. The second issue is a missing data problem, because the first and second month of a quarter are published before the corresponding quarterly data is available. A “nowcast” method can be used to estimate these months. The literature on mixed frequency models provides solutions for both problems, sometimes by dealing with them simultaneously. In this article we combine different benchmarking and nowcasting models and evaluate combinations. Our evaluation distinguishes between relatively stable periods and periods during and after a crisis because different approaches might be optimal under these two conditions. We find that during stable periods the so-called Bridge models perform slightly better than the alternatives considered. Until about fifteen months after a crisis, the models that rely heavier on historic patterns such as the Bridge, MIDAS and structural time series models are outperformed by more straightforward (S)ARIMA approaches.

Are low frequency macroeconomic variables important for high frequency electricity prices?

We analyse the importance of low frequency hard and soft macroeconomic information, respectively the industrial production index and the manufacturing Purchasing Managers' Index surveys, for forecasting high-frequency daily electricity prices in two of the main European markets, Germany and Italy. We do that by means of mixed-frequency models, introducing a Bayesian approach to reverse unrestricted MIDAS models (RU-MIDAS). Despite the general parsimonious structure of standard MIDAS models, the RU-MIDAS has a large set of parameters when several predictors are considered simultaneously and Bayesian inference is useful for imposing parameter restrictions. We study the forecasting accuracy for different horizons (from $1$ day ahead to $28$ days ahead) and by considering different specifications of the models. Results indicate that the macroeconomic low frequency variables are more important for short horizons than for longer horizons. Moreover, accuracy increases by combining hard and soft information, and using only surveys gives less accurate forecasts than using only industrial production data.

Measuring the response of clean energy stock price volatility to extreme shocks

The development of clean energy has made the green finance market attractive to investors, but existing studies lack an analysis of the impact of uncertain environmental shocks on the volatility of green finance stocks. This paper focuses on the impact of major events on clean energy stock returns by using a mixed-frequency model. Specifically, to identify asymmetric effects and extreme information spillovers, we construct extreme positive returns/positive returns and extreme negative returns/negative returns, respectively. The in-sample findings suggest that asymmetric effects and extreme shocks contain valid information about future clean energy stock price volatility. The out-of-sample analysis shows that the extended model can successfully predict the volatility of clean energy stock markets. More importantly, the extended model can generate predictive gains from both statistical and economic aspects. This study can provide a reference for implementing and adjusting energy policies, which is important for optimizing the energy structure and developing the green energy industry.

The impact of institutional analyst forecast divergence on crude oil market: Evidence from the mixed frequency models

As important information intermediaries, analysts play a non-negligible role in the crude oil market. Existing research often focuses on analysts' collection and interpretation of firm-specific information, but neglects the impact of analysts' forecasts on specific markets such as the crude oil market, which is crucial to the safe and stable development of the crude oil market. Therefore, this study uses historical data from January 2011 to December 2020 as a sample to construct analysts' forecast divergence indicators from 15 institutional analysts' forecast data on international crude oil futures prices. It then explores the impact of institutional analysts' forecast divergence on oil price return volatility, crude oil market jumps and crude oil futures trading volume, based on various mixed-frequency models. The results are as follows: First, volatility in oil price returns increases with a growing divergence in analysts' forecasts. Second, analysts' forecasts do not trigger jump in the crude oil market on the first six days after the information is released, but trigger a significant positive jump in the market on the seventh day. Third, the impact of analysts' forecast divergence on trading volume is weak; however, the reverse effect is significant, while the static and dynamic spillover results are consistent.

Real-time density nowcasts of US inflation: A model combination approach

We develop a flexible modeling framework to produce density nowcasts for US inflation at a trading-day frequency. Our framework (1) combines individual density nowcasts from three classes of parsimonious mixed-frequency models; (2) adopts a novel flexible treatment in the use of the aggregation function; and (3) permits dynamic model averaging via the use of weights that are updated based on learning from past performance. These features provide density nowcasts that can potentially accommodate non-Gaussian properties. We document the competitive properties of the nowcasts generated from our framework using high-frequency real-time data over the period 2000–2015.

Modelling returns volatility: mixed-frequency model based on momentum of predictability

The estimation and prediction of financial asset volatility are important in terms of theoretical and practical applications. Considering that low-frequency and high-frequency information plays an important role in volatility prediction, this article proposes a mixed-frequency model based on the momentum of predictability (MF-MoP). To illustrate the advantages of the proposed model, comparative research is conducted on the prediction accuracy of volatility among the GARCH model, the Realized GARCH model and the MF-MoP model, by the loss function and MCS test. The empirical results show that the MF-MoP model has higher prediction accuracy than the other two models; especially based on skewed-t distribution, the MF-MoP significantly outperforms the competing models. Moreover, the MF-MoP model can improve the forecasting of volatility, regardless of different look-back periods (including 1, 3, 6 and 9 days), different data (including the CSI 300 index, the N225 index and the KS11 index), and realized measures (including RV, RRV and MedRV), indicating that the model is robust.

A novel ensemble model based on artificial intelligence and mixed-frequency techniques for wind speed forecasting

Wind speed forecasting is of prime importance for wind power generation, which can bring tremendous economic, social and environmental benefits. However, previous wind speed forecasting studies mainly focused on proposing hybrid or ensemble models by combining different methods while ignoring the significant opportunities brought by the era of big data. In particular, the research and applications of mixed-frequency data modeling for wind speed forecasting are almost nonexistent, so some valuable issues remain and need to be studied in depth. In this context, a novel ensemble model, which successfully introduces mixed-frequency data into the field of wind speed forecasting and combines the merits of mixed-frequency models and artificial intelligence methods, is developed for wind speed forecasting. More specifically, the original wind speed data are preprocessed by an advanced data decomposition technique to effectively tackle the challenges caused by noise and capture the main characteristics that existed in the original data. Moreover, some artificial intelligence models and mixed-frequency models are designed as sub-models and employed to predict future wind speed changes; these models aim to make full use of the information existing in common-frequency and mixed-frequency data. Furthermore, a new ensemble forecasting model is developed by combining the power of kernel-based extreme learning machine and multi-objective optimization to ensemble the results output by the sub-models. Various experiments and discussions are designed using four seasons of data, and the proposed model achieves excellent forecasting results. For example, the mean absolute percentage errors of the proposed model are 4.4286%, 6.6154%, 5.2740% and 3.8682% for wind speed forecasting during the four seasons, proving the superiority of the developed model and the innovations and contributions provided by this study from different perspectives.

Analyzing and forecasting Thai macroeconomic data using mixed-frequency approach

Macroeconomic data are an important piece of information in decision making for both the public and private sectors in Thailand. However, the release of key macroeconomic data, usually in a lower frequency such as quarterly, is not always in a timely manner. Using the higher frequency data such as monthly and daily to analyze or forecast the lower frequency data can mitigate the release timing effect. This study applies the mixed-frequency data approach to analyze and forecast Thai key macroeconomic data. The mixed data sampling regressions with various specifications are employed and implemented through some macroeconomic data such as gross domestic product and inflation. The results show that in most cases the mixed-frequency models outperform the autoregressive integrated moving average model, which we used as the benchmark model, even during the COVID-19 period. Some policy implications can also be drawn from the analysis.

Boosting tax revenues with mixed-frequency data in the aftermath of COVID-19: The case of New York

We forecast New York state tax revenues with a mixed-frequency model using several machine learning techniques. We found that boosting with two dynamic factors extracted from a select list of New York and U.S. leading indicators did best to correctly update revenues for the fiscal year in direct multi-step out-of-sample forecasts. These forecasts were found to be informationally efficient over 18 monthly horizons. In addition to boosting with factors, we also studied the advisability of restricting boosting to select the most recent macro variables to capture abrupt structural changes. Since the COVID-19 pandemic upended all government budgets, our boosted forecasts were used to monitor revenues in real-time for the fiscal year 2021. Our estimates showed a drastic year-over-year decline in actual revenues by over 16% in May 2020, followed by several upward nowcast revisions that led to a recovery of −1% in March 2021, which was close to the actual annual value of −1.6%.

Nowcasting inflation in India with daily crowd-sourced prices using dynamic factors and mixed frequency models

ABSTRACT In this paper, we forecast short-term monthly headline retail inflation in India using daily crowd-sourced food prices and high frequency market-based measures by employing dynamic factors and mixed frequency models. We demonstrate that the forecast using the proposed approach outperforms the forecasts using the conventional approaches. The retail inflation rate for the last month is usually released around the mid of the current month. Hence, there is a delay in the availability of this critical metric. In this context, we leverage the intra-period high frequency data as it becomes available to improve forecast (nowcast) performance, which can be made available much before the official data release.

A comparison of monthly global indicators for forecasting growth

This paper evaluates the predictive content of a set of alternative monthly indicators of global economic activity for nowcasting and forecasting quarterly world real GDP growth using mixed-frequency models. It shows that a recently proposed indicator that covers multiple dimensions of the global economy consistently produces substantial improvements in forecasting accuracy, while other monthly measures have more mixed success. Specifically, the best-performing model yields impressive gains with MSPE reductions of up to 34% at short horizons and up to 13% at long horizons relative to an autoregressive benchmark. The global economic conditions indicator also contains valuable information for assessing the current and future state of the economy for a set of individual countries and groups of countries. This indicator is used to track the evolution of the nowcasts for the U.S., the OECD area, and the world economy during the COVID-19 pandemic and the main factors that drive the nowcasts are quantified.

Analyzing and Forecasting Thai Macroeconomic Data Using Mixed-Frequency Approach

Macroeconomic data are an important piece of information in decision making for both the public and private sectors in Thailand. However, the release of key macroeconomic data, usually in a lower frequency such as quarterly, is not always in a timely manner. Using the higher frequency data such as monthly and daily to analyze or forecast the lower frequency data can mitigate the release timing effect. This study applies the mixed-frequency data approach to analyze and forecast Thai key macroeconomic data. The mixed data sampling regressions with various specifications are employed and implemented through some macroeconomic data such as gross domestic product and inflation. The results show that in most cases the mixed-frequency models outperform the autoregressive integrated moving average model, which we used as the benchmark model, evenduring the COVID-19 period. Some policy implications can also be drawn from the analysis.

TF-MIDAS: a transfer function based mixed-frequency model

ABSTRACT This paper tackles the mixed-frequency modelling problem from a new perspective. Instead of drawing upon the common distributed lag polynomial model, we use a transfer function representation to develop a new type of models, named TF-MIDAS. We derive the theoretical TF-MIDAS implied by the high-frequency VARMA family models for two common aggregation schemes, flow and stock. This exact correspondence leads to potential gains in terms of nowcasting and forecasting performance against the current alternatives. The estimation of the model proposed is also addressed via its state space equivalent form. A Monte Carlo simulation exercise confirms that TF-MIDAS beats U-MIDAS models (its natural competitor) in terms of out-of-sample nowcasting performance for several data generating high-frequency processes.