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on Econometric Time Series |
| By: | Palumbo, D. |
| Abstract: | The occurrence of extreme observations in a time series depends on the heaviness of the tails of its distribution. The paper proposes a dynamic conditional score model (DCS) for modelling dynamic shape parameters that govern the tail index. The model is based on the Generalised t family of conditional distributions, allowing for the presence of asymmetric tails and therefore the possibility of specifying different dynamics for the left and right tail indices. The paper examines through simulations both the convergence properties of the model and the implications of the link functions used. In addition the paper introduces and studies the size and power properties of a new Lagrange Multiplier (LM) test based on fitted scores to detect the presence of dynamics in the tail index parameter. The paper also shows that the novel LM test is more effective than existing tests based on fitted scores. The model is fitted to Equity Indices and Credit Default Swaps returns. It is found that the tail index for equities has dynamics driven mainly by either the upper or lower tail depending if leverage is taken or not into account. In the case of Credit Default Swaps the test identifies very persistent dynamics for both the tails. Finally the implications of dynamic tail indices for the estimated conditional distribution are assessed in terms of conditional distribution forecasting showing that the novel model predicts more accurately expected shortfalls and value-at-risk than existing models. |
| Keywords: | Heavy Tailed Distributions, Extreme Events, Score-Driven Models, Tail Index, Lagrange Multiplier Test, Financial Markets |
| JEL: | C12 C18 C51 C52 C46 C58 G12 |
| Date: | 2021–01–29 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:2111&r=all |
| By: | Paulo M.M. Rodrigues; Marina Balboa; Antonio Rubia; A. M. Robert Taylor |
| Abstract: | We introduce a new joint test for the order of fractional integration of a multivariate fractionally integrated vector autoregressive [FIVAR] time series based on applying the Lagrange multiplier principle to a feasible generalised least squares estimate of the FIVAR model obtained under the null hypothesis. A key feature of the test we propose is that it is constructed using a heteroskedasticity-robust estimate of the variance matrix. As a result, the test has a standard 2 limiting null distribution under considerably weaker conditions on the innovations than are permitted in the extant literature. Specifically, we allow the innovations driving the FIVAR model to follow a vector martingale difference sequence allowing for both serial and crosssectional dependence in the conditional second-order moments. We also do not constrain the order of fractional integration of each element of the series to lie in a particular region, thereby allowing for both stationary and non-stationary dynamics, nor do we assume any particular distribution for the innovations. A Monte Carlo study demonstrates that our proposed tests avoid the large over-sizing problems seen with extant tests when conditional heteroskedasticity is present in the data. We report an empirical case study for a sample of major U.S. stocks investigating the order of fractional integration in trading volume and different measures of volatility in returns, including realized variance. Our results suggest that both return volatility and trading volume are fractionally integrated, but with the former generally found to be more persistent (having a higher fractional exponent) than the latter, when more reliable proxies for volatility such as the range or realized variance are used. |
| JEL: | C12 C22 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:ptu:wpaper:w202102&r=all |
| By: | Pablo Montero-Manso; Rob J Hyndman |
| Abstract: | Forecasting of groups of time series (e.g. demand for multiple products offered by a retailer, server loads within a data center or the number of completed ride shares in zones within a city) can be approached locally, by considering each time series as a separate regression task and fitting a function to each, or globally, by fitting a single function to all time series in the set. While global methods can outperform local for groups composed of similar time series, recent empirical evidence shows surprisingly good performance on heterogeneous groups. This suggests a more general applicability of global methods, potentially leading to more accurate tools and new scenarios to study. However, the evidence has been of empirical nature and a more fundamental study is required. Formalizing the setting of forecasting a set of time series with local and global methods, we provide the following contributions: • We show that global methods are not more restrictive than local methods for time series forecasting, a result which does not apply to sets of regression problems in general. Global and local methods can produce the same forecasts without any assumptions about similarity of the series in the set, therefore global models can succeed in a wider range of problems than previously thought. • We derive basic generalization bounds for local and global algorithms, linking global models to pre-existing results in multi-task learning: We find that the complexity of local methods grows with the size of the set while it remains constant for global methods. Global algorithms can afford to be quite complex and still benefit from better generalization error than local methods for large datasets. These bounds serve to clarify and support recent experimental results in the area of time series forecasting, and guide the design of new algorithms. For the specific class of limited-memory autoregressive models, this bound leads to the design of global models with much larger memory than what is effective for local methods. • The findings are supported by an extensive empirical study. We show that purposely naïve algorithms derived from these principles, such as global linear models fit by least squares, deep networks or even high order polynomials, result in superior accuracy in benchmark datasets. In particular, global linear models show an unreasonable effectiveness, providing competitive forecasting accuracy with far fewer parameters than the simplest of local methods. Empirical evidence points towards global models being able to automatically learn long memory patterns and related effects that are only available to local models if introduced manually. |
| Keywords: | time series, forecasting, generalization, global, local, cross-learning, pooled regression |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2020-45&r=all |
| By: | Ken Chung; Anthony Bellotti |
| Abstract: | This paper investigates the phenomenon of support and resistance levels (SR levels) in financial time series, which act as temporary price barriers that reverses price trends. We develop a heuristic discovery algorithm for this purpose, to discover and evaluate SR levels for intraday price series. Our simple approach discovers SR levels which are able to reverse price trends statistically significantly. Asset price entering SR levels with higher number of price bounces before are more likely to bounce on such SR levels again. We also show that the decay aspect of the discovered SR levels as decreasing probability of price bounce over time. We conclude SR levels are features in financial time series are not explained simply by AR(1) processes, stationary or otherwise; and that they contribute to the temporary predictability and stationarity of the investigated price series. |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2101.07410&r=all |
| By: | Pincheira, Pablo; Hardy, Nicolás; Muñoz, Felipe |
| Abstract: | In this paper we present a new asymptotically normal test for out-of-sample evaluation in nested models. Our approach is a simple modification of a traditional encompassing test that is commonly known as Clark and West test (CW). The key point of our strategy is to introduce an independent random variable that prevents the traditional CW test from becoming degenerate under the null hypothesis of equal predictive ability. Using the approach developed by West (1996), we show that in our test the impact of parameter estimation uncertainty vanishes asymptotically. Using a variety of Monte Carlo simulations in iterated multi-step-ahead forecasts we evaluate our test and CW in terms of size and power. These simulations reveal that our approach is reasonably well-sized even at long horizons when CW may present severe size distortions. In terms of power, results are mixed but CW has an edge over our approach. Finally, we illustrate the use of our test with an empirical application in the context of the commodity currencies literature. |
| Keywords: | forecasting; random walk; out-of-sample; prediction; mean square prediction error |
| JEL: | C01 C1 C12 G17 |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:105368&r=all |
| By: | Racine Ly; Fousseini Traore; Khadim Dia |
| Abstract: | This paper applies a recurrent neural network (RNN) method to forecast cotton and oil prices. We show how these new tools from machine learning, particularly Long-Short Term Memory (LSTM) models, complement traditional methods. Our results show that machine learning methods fit reasonably well the data but do not outperform systematically classical methods such as Autoregressive Integrated Moving Average (ARIMA) models in terms of out of sample forecasts. However, averaging the forecasts from the two type of models provide better results compared to either method. Compared to the ARIMA and the LSTM, the Root Mean Squared Error (RMSE) of the average forecast was 0.21 and 21.49 percent lower respectively for cotton. For oil, the forecast averaging does not provide improvements in terms of RMSE. We suggest using a forecast averaging method and extending our analysis to a wide range of commodity prices. |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2101.03087&r=all |
| By: | Leonard G\"oke; Mario Kendziorski |
| Abstract: | To manage computational complexity, models of macro-energy systems commonly deploy reduced sets of time-series data. This paper evaluates the adequacy of time-series reduction when modelling energy systems with fully renewable generation and a consequent dependency on storage. Analysis includes various methods to derive reduced time-series and to implement them into models, either as time-slices, also referred to as representative days, or continuous time-steps. All methods are tested with regard to unmet demand and accuracy of estimated system costs using a simple capacity expansion model of the power sector within a renewable energy system. Some methods achieve little unmet demand, but instead their results regarding storage are biased and favour seasonal at the expense of short-term storage. We conclude that renewable energy systems limit the adequacy of time-series reduction and future research should focus on alternative methods to reduce computational complexity. |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2101.06221&r=all |
| By: | Florian Eckert (KOF Swiss Economic Institute, ETH Zurich, Switzerland); Philipp Kronenberg (KOF Swiss Economic Institute, ETH Zurich, Switzerland); Heiner Mikosch (KOF Swiss Economic Institute, ETH Zurich, Switzerland); Stefan Neuwirth (KOF Swiss Economic Institute, ETH Zurich, Switzerland) |
| Abstract: | Most macroeconomic indicators failed to capture the sharp economic fluctuations dur- ing the Corona crisis in a timely manner. Instead, alternative high-frequency data have been used, aiming to monitor the economic situation. However, these data are often only loosely related to the business cycle and come with irregular patterns of missing observations, ragged edges and short histories. This paper presents a novel mixed- frequency dynamic factor model for measuring economic activity at high-frequency intervals in rich data environments. Previous research has estimated the dynamic factor conditional on actually observed data only. In contrast, we propose to estimate the dynamic factor conditional on a balanced panel with observed and latent data information, where the latent data are themselves estimated in a separate state-space block. One benefit of this data augmentation strategy is that it allows to easily ac- count for serial correlation in the factor measurement errors. We apply the model to a set of daily, weekly, monthly and quarterly series and extract a dynamic factor, which is identified as the weekly growth rate of GDP. It turns out that the model is well suited to exploit the business cycle information contained in alternative high- frequency data. GDP is tracked timely and accurately during the Corona crisis and past economic crises. |
| Keywords: | Economic Activity Indicator, Real Time, Nowcasting, Alternative HighFrequency Data, Mixed-Frequency Dynamic Factor Model, Data Augmentation |
| JEL: | C11 C32 C38 C53 E32 E37 |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:kof:wpskof:20-488&r=all |
| By: | Fajar, Muhammad; Prasetyo, Octavia Rizky; Nonalisa, Septiarida; Wahyudi, Wahyudi |
| Abstract: | The outbreak of COVID-19 is having a significant impact on the contraction of Indonesia`s economy, which is accompanied by an increase in unemployment. This study aims to predict the unemployment rate during the COVID-19 pandemic by making use of Google Trends data query share for the keyword “phk” (work termination) and former series from official labor force survey conducted by Badan Pusat Statistik (Statistics Indonesia). The method used is ARIMAX. The results of this study show that the ARIMAX model has good forecasting capabilities. This is indicated by the MAPE value of 13.46%. The forecast results show that during the COVID-19 pandemic period (March to June 2020) the open unemployment rate is expected to increase, with a range of 5.46% to 5.70%. The results of forecasting the open unemployment rate using ARIMAX during the COVID-19 period produce forecast values are consistent and close to reality, as an implication of using the Google Trends index query as an exogenous variable can capture the current conditions of a phenomenon that is happening. This implies that the time series model which is built based on the causal relationship between variables reflects current phenomenon if the required data is available and real-time, not only past historical data. |
| Keywords: | Unemployment, Google Trends, PHK, ARIMAX |
| JEL: | C22 C53 E24 E37 E39 J6 J64 |
| Date: | 2020–11–30 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:105042&r=all |