Hodrick-Prescott Filter Research Articles

Disentangling the asymmetric effect of financialization on the green output gap

Insufficient green output can lead to environmental degradation while overinvestment may result in economic imbalances, social inequalities, and opportunity costs. Thus, sustaining an optimal level of green growth could restrict both green neglect and green grabbing. A higher level of financialization is believed to be an efficient allocation mechanism for green development. This research provides empirical insights into how financialization helps narrow the green growth gap. Using various estimation techniques such as the Hodrick-Prescott (HP) filter, Hamilton's filter, and the super-efficiency slack-based model, we examine the heterogeneous effects of financialization on the green growth gap by utilizing unbalanced panel data from 124 countries spanning the period 1980–2020. The results, obtained through bootstrapped quantile regression, indicate that financial access, depth, and efficiency contribute to improving insufficient green growth levels and curbing excessive investment in green initiatives. However, we find little or no evidence that financial stability or liberalization restricts overinvestment in low-carbon economic development or improves environmental stewardship when green neglect is observed. Additional analysis suggests that business cycle fluctuations, especially during recessionary periods, adversely affect the ability of financialization to optimally allocate green resources, but this effect is mitigated if financial development is countercyclical. Policymakers should prioritize promoting financial depth and efficiency, as well as provide access to finance, in order to support sustainable green growth and to avoid overinvestment in low-carbon economic development.

HPX filter: a hybrid of Hodrick–Prescott filter and multiple regression

Abstract This paper considers an extension of Hodrick–Prescott (HP) filter. It is a hybrid of HP filter and multiple regression. We refer to the filter as “HPX filter”. It is well known that HP filter has a unique global minimizer and the solution can be represented in matrix notation explicitly. Does HPX filter also have a unique global minimizer? Is it accomplished without any additional assumptions? Can the solution be expressed in matrix notation explicitly? In this paper, we answer these questions. In addition, this paper (i) provides an alternative perspective on the filter by representing it as a generalized ridge regression and (ii) gives an extension of it, which is a hybrid of Whittaker–Henderson method of graduation and multiple regression.

The Asymmetric Effect of Trade Openness on Output Volatility: Empirical Evidence from Ethiopia

A better understanding of the effect openness on volatility can lead to more effective government policy that addresses the adverse outcomes of volatility. By using NARDL model, Hodrick-Prescott (HP) filter, and annual time-series data from the period 1981 to 2020, this study examined the effect of openness on output volatility in Ethiopia. From the NARDL bound test, the research find a long-run cointegration between output volatility, agricultural output, trade openness, lending rate, and money supply. We also found a long-run negative asymmetric effect, and short-run negative symmetric effect of openness on volatility—suggesting this open trading activity has a relationship that can reduce output volatility in Ethiopia. This possibility shows Ethiopia would benefit from international trade and openness reduces the adverse effects of volatility. Besides, we confirmed the positive asymmetric effect of agricultural output both in the long run and short run. The lending rate, that represents the cost of borrowing, has a positive effect on output volatility. The long-run and short-run coefficients of money supply have a negative and significant effect on output volatility.

Ensemble learning methods using the Hodrick–Prescott filter for fault forecasting in insulators of the electrical power grids

Electrical power grid insulators installed outdoors are exposed to environmental conditions, such as the accumulation of contaminants on their surface. The contaminants increase the surface conductivity of the insulators, increasing leakage current until there is a flashover. Evaluating the increase in leakage current in relation to the contamination level is one way to determine the insulation condition. This paper evaluates a time series of leakage current from a high-voltage laboratory experiment using porcelain pin-type insulators. Time series forecasting is performed with a collection of machine learning models known as ensemble learning approaches, which include blending, bootstrap aggregation (bagging), sequential learning (boosting), random subspace, and stacked generalization. According to this paper’s findings, applying these ensemble learning approaches is useful for enhancing the performance of the machine learning models in forecasting the occurrence of breakdowns in the electrical power system. The Hodrick–Prescott filter reduces the root mean square error performance metric (to be minimized) by 2.69 times using the ensemble random subspace approach. According to the results of this paper, the proposed method is stable, with low variance when a statistical analysis is performed, being superior to the long short-term memory neural network.

How do funding diversity and non-performing loans affect bank performance in different economic cycles?

This paper aims to study the impacts of bank funding diversity, non-performing loans (NPLs), and business cycles on bank performance. We employ Fixed Effect Models and the two-step system Generalized Method of Moments to examine a sample of 37 Vietnamese banks from 2005 to 2020. Our findings report that a one percentage point increase in the funding diversity index empowers ROA by 0.031 percentage points. Our results indicate that one positive standard deviation of real GDP from the trend calculated by the Hodrick-Prescott filter increases the ROA by 0.004 percentage points. However, a percentage point increase in non-performing loans reduces ROA by 0.075 percentage points. Our findings are also robust in various proxies of bank performance, economic cycles, and FED interest rate cycles. The findings help determine the optimal funding strategy for policymakers and bank managers. These findings suggest that bank managers develop long-term credit policies to control NPLs, improving sustainable performance. Regulators closely monitor macroeconomic factors to maintain banking stability in different economic stages. Our findings align with the diversification theory, trade-off theory, and prior literature.

Nexus of Fiscal Instability and Developmental Outcomes in Nigeria

This paper examines the effect of fiscal instability component on the fluctuation in welfare indicator for 45 years. Descriptive statistics reveals that fiscal component and real GDP per capital are largely unstable and Hodrick-Prescott filter (HPF) is employed as a smoothing measure of the long-term component. Descriptive statistics reveals that lesser government revenue had been committed to the development purposes compared with recurrent expenditure since the beginning of the fourth republic in Nigeria. Using ARDL model, the study found that, there exist a long-run association among the variable of interest as one percent increase in the rate of instability in recurrent expenditure led to an approximate of 30% reduction in the fluctuation of the welfare indicator while instability in the capital expenditure led to 36% increase in the fluctuation of the GDP per capital. In the short-run however, 1% increase in the immediate lagged value of cyclical capital expenditure had significantly increase the fluctuation in the current welfare index by 54% but such effect is reduced to 43% in two-year lagged. Also, one percent increase in the immediate lagged value of instability in the recurrent government expenditure had significantly reduced the fluctuation in the GDP per capital by 21% but only 9% of such reduction was off set in the two-year lagged. The study therefore, recommended greater control of instability in the fiscal components through diversification revenue base should be emphasized in other to stabilize the fluctuation of the welfare indicator in the short-run and long-run.

Comments on the Oyster Aquaculture Industry in China: 1985-2020.

Since the 1980s, China's oyster aquaculture has grown quickly in the past four decades, and it became the top mariculture species in China with an annual production of 5.23million in 2019. Understanding the growth of oyster aquaculture in China is important to gain insights into successful long-term production. This paper attempts to decompose China's oyster aquaculture between trends and cycles by means of an HP filter, make a specific identification of the relevant factors according to the Cobb-Douglas production function, to summarize the objective law of yield fluctuations. Results suggest that from 1985 to 2011, China's oyster aquaculture experienced a development stage of "rapid rise - steady development". At this stage, it shows a slow growth trend, and the growth can persist for long periods of time. The improvement of consumption level driven by economic growth is the main facilitating factor to promote the oyster industry, export trade and oyster price are also critical, diseases and disasters did not exert much influence on the growth of China's oyster aquaculture. The biggest problem hindering sustainable development is the tragedy of the commons caused by the limitation of marine resources, the contradiction of development will become a thorny issue.

Modelling output gaps in the Euro Area with structural breaks: The COVID-19 recession

This paper proposes a novel unobserved component model with a COVID-19 structural break in the trend growth rate to model output gaps. Using historical real GDP data for the Euro Area between 1995Q1 and 2022Q1, we test our framework against a battery of competing models, including a standard unobserved components model, a correlated model with a second-order Markov process, a Hodrick–Prescott filter and an augmented version of it. To examine the impact on the fitting performance, we test the inclusion and exclusion of pandemic quarters and we also extend the estimation to a country-level detail. We find that: (i) our suggested model outperforms the competing ones; (ii) when excluding pandemic quarters, the standard unobserved component model outperforms their counterparts; (iii) our model yields the best fitting performance for most of the Euro Area countries and (iv) the Hodrick–Prescott filter model has the poorest fitting performance.

Estimating the Business Cycle of Ukraine Under the Conditions of Large External Compound Shocks

Abstract. Introduction. Conventional business cycle estimation methods typically rely on the assumption that the shocks to an economy are normally distributed. However, global social and political instability can result in external shocks that are more severe than purely economic shocks, thus hampering the ability of these estimation methods to separate cyclical behavior from long-run dynamics. Since effective economic policy is dependent upon the ability to make accurate forecasts, an understanding of the properties of business cycle estimation methods in the presence of large shocks in the data is of first order importance. Purpose. The purpose of this article was to compare the ability of various business cycle estimation methods — and in particular detrending filters — to account for large external compound shocks (i.e. those containing both economic and noneconomic components) when extracting the cyclical component of the real GDP series of Ukraine. In view of Ukraine’s policy of European integration, a secondary goal was to investigate the performance of various detrending filters in deriving a measure of business cycle co-movement of Ukraine vis-à-vis the EU that is robust to external compound shocks. Results. Using an unobserved components model with external geopolitical shocks as a benchmark, it was found that the application of the boosted Hodrick-Prescott filter, the Christiano-Fitzgerald filter, and the Hamilton regression filter to the real GDP data of Ukraine produced cyclical components that exhibited spurious dynamics, particularly from 2020 and onward. Conclusions. It was shown that no single business cycle estimation method performed the best in application to the real GDP series of Ukraine. While the unobserved components model relied on extensive researcher-specified assumptions and an ad hoc approach to identifying external compound shocks, the use of data filtering resulted in series that did not accurately reflect cyclical and trend dynamics in Ukraine toward the end of the sample. Thus, there is a practical need to develop new business cycle estimation models that would be able to account for the distorting influence of large external compound shocks.

Multilevel Residual Prophet Network Time Series Model for Prediction of Irregularities on High-Speed Railway Track

Accurate prediction of the change in track irregularity plays an essential role in keeping the high-speed railway safe and stable. Regular maintenance is an important measure to guarantee track smoothness, which has a great influence on the change of track state. This paper introduces the time series anomaly detection model (AD) to detect changes by tracking the difference between the mean values of two sliding time windows. These changes are taken as one of the holidays of the prophet model which is called the AD_ Prophet model. Moreover, this paper proposes a multilevel residual prophet (Re-Prophet) prediction network which can make full use of the information of residual data to predict the results. The final predicted result is the sum of the value of each prediction. To explore the characteristics of the time series, the Hodrick-Prescott filter is used to explore the trend. A multi-month-wise box plot is used to explore the seasonal volatility and the wavelet transform is used to explore the cyclical variation. Based on these characteristics, the fitting model can be chosen. Finally, to verify the high accuracy of the model, the surface irregularities of the high-speed railway are used as the research objects. Compared with conventional prediction algorithms, the proposed model has the smallest prediction deviation and the highest accuracy based on the evaluation indicators such as mean squared error, root mean squared error, mean absolute error, and mean absolute percentage error.

A dataset of the HP filter model-based research on price volatility of solanaceous vegetables in Beijing Xinfadi Market from 2012 to 2018

Solanaceous vegetables are popular dishes for residents, and they are also one type of the important cultivated vegetables in China. The price of solanaceous vegetables is non-steady with large fluctuations. Therefore, it is important to master the historical price trends and fluctuation laws, which can provide scientific guidance and support for ensuring the stability of vegetable supply prices and guiding the orderly operation of the market. Through data collection, stability test and HP filtering method decomposition, we formed a dataset of the HP filter model-based research on price volatility of solanaceous vegetables at Beijing Xinfadi Agricultural and Sideline Products Wholesale Market from 2012 to 2018. The varieties cover five kinds of solanaceous vegetables (eggplant, tomato, green pepper, bean and cucumber), including market, date, weekly/monthly average price, weekly/monthly average volatility, weekly/monthly maximum price, weekly/monthly minimum price, weekly/monthly average HP filter trend value, weekly/monthly average HP filter fluctuation value. The dataset can reflect the weekly and monthly changes of the trading prices of solanaceous vegetables in Beijing Xinfadi Market, and provide scientific data foundation for the research on as well as monitoring and early warning of the price fluctuation of solanaceous vegetables in Beijing.

THE DYNAMIC OF INDONESIA’S SECTORAL ECONOMIC CYCLES

The purpose of this study is to observe the dynamic of Indonesia’s economic cycles for six main sectors. In constructing the cycles, we use quarterly gross domestic product (GDP) for six Indonesian sectors over the period 2000-2021. We obtain the economic cycles for each of the six sectors using Hodrick-Prescott filter and Christiano-Fitzgerald filter techniques. We find evidence that five of six sectors have relatively strong correlation with the aggregate GDP growth cycle. Additionally, by using the concordance index, we further conclude that three sectors are pro-cyclical with the aggregate GDP growth cycle.

Stock price valuation analysis of the digital technology industry based on the HP-ARIMA method - with 18 listed companies of different volume sizes in its 3 segments as an example

The world securities market has formed a more complete system since its origin in the 17th century, with a considerable number of small and medium-sized investors and institutional investors, and proposing innovative new methods for securities valuation models can assist investors in making more accurate investment decisions. This paper proposes for the first time to use an interdisciplinary analysis method, ARIMA + HP filter analysis, to analyze the valuation of the securities market, by taking the opening prices of individual stocks in digital technology industry segments: blockchain, artificial intelligence, and Beidou navigation as examples for valuation analysis, firstly, the initial data of the opening prices of individual stocks from 2019-2021 are analyzed by HP filter analysis, and secondly, the data are analyzed while doing Tobit model test. By analyzing the long-term trend of the digital technology industry after noise reduction, its corresponding valuation forecast and value judgment results show that the head effect of the digital technology industry is more significant, and the opening price volatility shows a U-shaped relationship with company size and profitability, and the opening price volatility of individual stocks is less, while the shorter the company's establishment time, the greater the stock price volatility. While the past literature focused on the traditional valuation of financial conditions and historical data analysis of a single variable, this paper analyzes the data of individual stocks in the digital technology industry through an interdisciplinary analysis method, which allows for a more comprehensive use of historical data and prediction of possible stochastic fluctuations, providing a more reliable valuation method for securities investors and opening up new ideas for research related to the field of valuation analysis.

Credit gaps as banking crisis predictors: A different tune for middle- and low-income countries

The aim of this paper is to assess the quality of credit-based variables as early warning indicators of systemic banking crises. The existing literature focuses mainly on developed economies and shows that the best performing indicator is the credit-to-GDP gap computed via one-sided HP filter (the so-called Basel credit gap). The empirical evidence legitimates the use of the credit-to-GDP gap as a key indicator in macro-prudential banking regulation, i.e., in the determination of the countercyclical capital buffer. We take advantage of a new database on bank credit series and credit gaps covering more than 160 countries (Bouvatier, Delatte and Rehault, 2022) to focus specifically on middle- and low-income countries. Our findings suggest that the credit-to-GDP gap remains the single best performing indicator regarding the high-income group while the same does not hold for middle- and low-income countries. This result highlights that a one-size-fits-all approach is not relevant in the design of the operational framework of the countercyclical capital buffer. Further, we show that the credit gap turns to be a fair banking crises predictor when the financial development, captured by the trend’s value in credit-to-GDP ratio, exceeds 20%.

Multi-Reservoir Echo State Networks with Hodrick–Prescott Filter for nonlinear time-series prediction

The Echo State Network (ESN) is a representative model for reservoir computing, which is capable of high-speed model training for machine learning tasks with time series data. Extended models of the ESN, such as Multi-Reservoir ESNs (MRESNs), have been intensively studied for performance improvement in recent years. In this study, we propose a new model called an HP-MRESN by combining an MRESN with the Hodrick–Prescott (HP) filter for nonlinear time series prediction. The proposed HP-MRESN comprises three basic components: a time series decomposer, a reservoir state extractor, and an ensemble decoder. In the time series decomposer, we recursively leverage the HP filter to decompose original time-series data into multiple trend and cycle components. In the reservoir state extractor, each time series component is fed into a corresponding reservoir-state encoder for generating a reservoir state which is extracted as it is or through the principal component analysis. In the ensemble decoder, the states of multiple reservoirs are collected and processed to produce model outputs. Moreover, we propose a greedy algorithm to automatically find the best model architectures under designated hyperparameters for different prediction tasks. Experimental results on a total of 24 nonlinear time-series prediction tasks with 6 real-world datasets demonstrate that our proposed HP-MRESN not only can outperform some existing representative MRESN models and fully-trained RNN models but also can have relatively low training time. In addition, performance comparisons between the HP-MRESN and related MRESN models with other prepossessing methods show the benefit of time series decompositions using the HP filter. The codes of the proposed method are publicly available on https://github.com/Ziqiang-IRCN/HP-MRESN.

Empirical impact of China-Pak business cycle synchronization on environmental degradation in Pakistan

This study investigates the empirical impact of China-Pak business cycle synchronization, urbanization, foreign direct investment, exports, and imports on environmental degradation in Pakistan from 1975 to 2017. In doing so, we use the Hodrick-Prescott filter to obtain the trend component of GDP. Then the trend component is subtracted from the original series of GDP to capture the cyclical component of China and Pakistan. The business cycle synchronization index is used to estimate synchronization between the business cycles of both countries. Using the ARDL method, we investigate the existence of a long-run co-integration relationship between the variables of interest. The empirical findings indicate that all explanatory variables (except FDI) are found to be significant factors of environmental degradation in the model. Furthermore, both imports and urbanization have a positive and significant impact on environmental degradation in Pakistan. At the same time, China-Pak business cycle synchronization and exports are discovered to have negative and significant coefficients for environmental degradation in Pakistan. The negative and significant ECM value indicates model convergence and a short-run relationship. The findings of the study suggest that improvement in China-Pak business cycle synchronization may be a factor that promotes environmental sustainability in Pakistan. An increase in exports and a decrease in imports can significantly contribute to reducing environmental degradation in Pakistan. A favorable balance of payment can provide sufficient financial prosperity to take environmental preservation measures. Policymakers should create effective urban planning, which has the potential to improve the country’s environmental quality.

How credible are Okun coefficients? The gap version of Okun’s law for G7 economies

The paper draws attention to the fact that findings that follow from estimation of Okun’s law are extremely sensitive to methodological choices. The argument rests in a case study oriented upon G7 countries for a period 1991/Q1–2021/Q4 and accounts for a possible asymmetry in the output–unemployment relationship. First, business and unemployment fluctuations are estimated by six purely statistical approaches that arise by casting the Hodrick–Prescott filter, the Hamilton filter and the unobserved component model into a univariate or bivariate framework. Second, the gap version of Okun’s law is modelled by means of an auto-regressive distributed lag model or its nonlinear threshold counterpart according as asymmetry is allowed or not. The results indicate huge heterogeneity in Okun coefficients for every country caused by differences even in the basal methodological aspects accounted for in the case study. The diversity of results demonstrates that initial modelling choices may provide economic policy-makers with conflicting insights and advice. This issue follows merely from the absence of general standards that might decide which particular result is more credible.

The Holt–Winters filter and the one-sided HP filter: A close correspondence

We show that the trend of the one-sided HP filter can be asymptotically approximated by the Holt–Winters (HW) filter. The latter is an elegant, moving average representation and facilitates the computation of trends tremendously. We confirm the accuracy of this approximation empirically by comparing the one-sided HP filter with the HW filter for generating credit-to-GDP gaps. We find negligible differences, most of them concentrated at the beginning of the sample.

Analysis of Turkey’s Detrending Economics Using the Hodrick-Prescott Filter

This paper aims to analyze the effectiveness of detrending policies in Turkey using the Hodrick- Prescott (HP) filter, the country’s Gross Domestic Product (GDP), and selected indicators from 2010 to 2021. The HP filter is a commonly used statistical tool for detrending time series data by separating the trend component from the cyclical component of a series. The discussion section shows the observable and physical impact of overlooking the cyclical components over the trend components. It also contains verifiable facts from several trustworthy sources showing the precise impact of detrending the economy. The final section of this work contains the final results and recommendations that make up the entirety of this work’s body. By analyzing the trend in GDP and selected indicators such as inflation, exchange rate, and unemployment rate, we can gain insights into how Turkey’s economy has been affected by detrending policies; and provides a basis from which better policies can be founded.

A hybrid forecasting technique for infection and death from the mpox virus.

The rising of new cases and death counts from the mpox virus (MPV) is alarming. In order to mitigate the impact of the MPV it is essential to have information of the virus's future position using more precise time series and stochastic models. In this present study, a hybrid forecasting system has been developed for new cases and death counts for MPV infection using the world daily cumulative confirmed and death series. The original cumulative series was decomposed into new two subseries, such as a trend component and a stochastic series using the Hodrick-Prescott filter. To assess the efficacy of the proposed models, a comparative analysis with several widely recognized benchmark models, including auto-regressive (AR) model, auto-regressive moving average (ARMA) model, non-parametric auto-regressive (NPAR) model and artificial neural network (ANN), was performed. The introduction of two novel hybrid models, and , which demonstrated superior performance compared to all other models, as evidenced by their remarkable results in key performance indicators such as root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE), is a significant advancement in disease prediction. The new models developed can be implemented in forecasting other diseases in the future. To address the current situation effectively, governments and stakeholders must implement significant changes to ensure strict adherence to standard operating procedures (SOPs) by the public. Given the anticipated continuation of increasing trends in the coming days, these measures are essential for mitigating the impact of the outbreak.