Boosting the Hodrick-Prescott Filter

Temporal Aggregation, Systematic Sampling, and the Hodrick-Prescott Filter

The role of detrending methods in a model of real business cycles

The current paper extends previous results on Hodrick–Prescott (HP) filtering and shows that it is possible to implement the judgement-augmented, or restricted, HP filter within the state-space framework. The implementation entails augmenting the vector of measurements and altering one of the system matrices of the state-space model for the HP filter. Restrictions can thereby be incorporated in the HP filter, making, e.g., estimation more accessible. An application to US GDP gap estimation illustrates how the restricted filter could be usefully applied in an empirical macroeconomic setting.

The Hodrick–Prescott (HP) filter is a commonly used tool in macroeconomics to obtain the HP filter trend of a macroeconomic variable. In macroeconomics, the difference between the original series and this trend is called the ‘cyclical component’. In this article, we derive the autocovariance function and the spectrum of the cyclical component of a series that consists of a constant, a linear time trend, a unit root process, and a weakly stationary process. We show that the autocovariance function of the cyclical component of such a series depends on (i) the autocovariance of the innovations of the unit root process; (ii) the autocovariance of the weakly stationary process and; (iii) a component of the weights of the HP filter that is important in the middle of a large sample. The result for the spectrum of the cyclical component matches with earlier results in the literature that were obtained by using an approximate approach. Lastly, we derive the cross‐covariance function and the cross‐spectrum of the cyclical components of two cointegrated series.

Because Hodrick–Prescott (HP) filtering and ℓ1 trend filtering are expressed as penalized least squares problem, both of them require the specification of their tuning parameter. For HP filtering, we have accumulated knowledge for selecting the value of its tuning parameter. However, we do not have similar knowledge for ℓ1 trend filtering. This paper presents a new method for specifying the tuning parameter of ℓ1 trend filtering so that the sum of squared residuals of HP filtering and that of ℓ1 trend filtering may be equivalent.

This paper estimates Japan’s output gap using the recently developed l1 trend filter, which is an alternative to the popular Hodrick–Prescott (HP) filter. This new filter provides a piecewise linear trend line, which means it possibly provides better output gap estimates than the HP filter does for an economy such as Japan that has experienced some structural breaks.

Purpose – The purpose of this study is to investigate whether different types of service firms, experience-based or credence-based, benefit equally from the prescription to increase advertising during recessions. Design/methodology/approach – The research consists of three steps: using the Hodrick–Prescott (HP) filter to extract the cyclical component of the time series, estimating the level of cyclical comovement and estimating the relationship between comovement and stock price. Findings – The results suggest that experience-based service firms benefit financially from adopting the advertising “prescription” that encourages firms to increase advertising during recessions. Credence-based firms, however, experience negative financial returns when they implement the advertising “prescription”. Research limitations/implications – The limitations are data from US firms and a smaller sample size. The use of the HP filter may be considered a limitation, as other filtering methods may be utilized. The results suggest that academics’ and practitioners’ advertising “prescription” is not a one-size-fits-all strategy for service firms. Practical implications – Managers must be aware that the type of service their firm provides influences whether increasing or decreasing advertising spending during a recession has a positive or negative impact on financial performance. Credence-based firms, such as those in the banking and insurance industries should avoid increasing advertising spending during recessions, as it may lead to negative financial performance. Experience-based firms, such as those in the entertainment and travel industries, benefit financially from increased advertising during recessions. Originality/value – This research is first to investigate the differential impact of recessionary advertising on service firms.

Precipitation is one of the main hydrometeorological variables since it affects water resources, environment, and natural hazards like flood and drought. Due to the complexity and uncertainty of the precipitation, valid and reliable precipitation forecasting remains a challenge. This study aims to find the key features that are important in developing a valid model for rainfall forecasting. Multiple feature selection algorithms including ICAP, as an information theoretical-based algorithm, and fisher-score, as a similarity-based algorithm, are used to find principal features. In addition, the trend and cycle parts of the rainfall that are decomposed by the Hodrick-Prescott (HP) filter are simulated by the time series models and the machine learning algorithm, respectively. The hybrid model combining machine learning models (KNN, Random Forest) and time series models (AR, MA, ARIMA) is used to forecast rainfall. To find a proper set of features for precipitation forecasting model, different categories including, hydrological variables from NOAA and ECMWF, cloud properties from ISCCP, and large-scale atmospheric circulation from NOAA, are used to represent precipitation formation in different seasons. Indeed, different mechanisms of precipitation formation that varies in different seasons can be determined by a specific set of features. For instance, findings reveal that longwave radiation can be considered as a significant feature in fall season. Results show that although the key features vary in different periods due to different processes of precipitation formation in each season, large-scale circulation like the North Atlantic Oscillation (NAO) and the atmospheric pattern of ENSO (El Niño–Southern Oscillation) with cloud features are important in all seasons for the precipitation forecasting model. In addition, results indicate that the developed hybrid model for representing the trend (linear) and cycle (nonlinear) part of the rainfall achieves a high and satisfactory level of accuracy (R2 = 0.8). The high accuracy of the model highlights the role of the key features in precipitation forecasting and importance of linear and nonlinear parts of the rainfall that need to be considered and modeled properly. The product of precipitation forecasting can be used as the input and driver of other models like hydrologic and ecosystem models. In addition, the developed model can be efficiently used in flood warning system to reduce damage and losses. 

The study analysed the behaviour of potential output and output gap for the Namibian economyusing annual data from 1980 to 2016. The study employed the Hodrick-Prescott (HP) filter method and theproduction function approaches to estimate potential output before calculating the output gap. The resultssuggest an annual average growth rate of 3.6 percent in potential output. However, it has been noted that theaverage annual growth rate in potential output has been shifting during the period under review. In fact, theresults suggest an annual average growth rate of 1.6 percent between 1980 and 1985 and an increase to 2.5percent per year for the period 1986 to 1990. Potential output estimates obtained using the productionfunction approach was smooth and stable throughout the study period. The potential output estimatesobtained through the two methods follow the same cyclical movements. The output gap estimates from thetwo techniques are not different from each other, and they appear to move together.

This paper aims to analysis the cyclicity pattern and to estimates the effect of macroeconomics indicators on capital inflows in East Java. The first analysis by using Hodrick-Prescott (HP) filter shows that capital inflows in East Java have a tendency to move in procyclical pattern. While the second by using VAR analysis shows that macroeconomics indicators are dominant factor for investors to invest their funds in East Java. Likewise, this paper indicates the pattern of capital inflows in East Java is tend to procyclical. Moreover,the macroeconomics indicators that affect capital inflows in East Java are economic growth and inflation. Based on the result, this paper suggest for local governments to synchronize the development of capital inflows together with macroeconomics conditions. Furthermore, the capital inflows can be managed properly to avoid the “surges” and “sudden stop” phenomenon.

The strategic choice of Moroccan banks to conquer the African market has accelerated since the mid-2000s. According to the Banking Commission of the West African Economic and Monetary Union (WAEMU), Moroccan banks concentrate 29.6% of the market share in the WAEMU region in 2015, and more than 30% of the share of global net income in the region. The article is devoted to the research of the role of Moroccan banks in the economic development in African countries. Can Moroccan banks affect real economic activity and act as catalysts for financial and economic development in African countries? To answer this question, we examine the co-movements between loans granted by Moroccan banks in African countries and real activity in those countries. Therefore, we use the synchronization index proposed by Hading and Pagan (2002). The cycles were obtained with a Hodrick-Prescott (HP) filter. The concordance index values, cross-correlation values were used to identify the characteristics of the relationships between the cyclical components. The study covers the period 2006-2015 and focuses on three Moroccan banking groups (Attijariwafabank, BMCE Bank of Africa and Banque Centrale Populaire BCP) set up in seven countries: Benin, Burkina Faso, Cote d'Ivoire, Mali, Senegal, Togo and Niger. The empirical results revealed that the financial (credits granted by Moroccan banks) and business (real activity) cycles are highly synchronized in WAEMU. The study concluded that the bank credits have a positive impact on real activity in WAEMU countries within the period examined.

Illustrating extraordinary shocks causing trend breaks

Discussion on selecting the number of breaks in the pattern of spread of COVID-19 (a reply to Zhao and Liang)

The paper deals with assessing the common trends in business cycle similarity and convergence in Europe. The main goal of the paper is to identify common cyclical co-movements and trends in convergence among the European countries so that the emerging European business cycle could be identified. Concerning the factors of business cycle, the research question of the paper is based on assumption that the integration effects are so dominant to bring the European cycle into existence. Also a potential influence of the global crisis on European and world business cycles is examined in the paper. The industrial production index is used to approximate business cycles. Hodrick-Prescott filter, Christiano-Fitzgerald filter and first differencing were used to dissect the cyclical components and identify the cycles in the data. The co-movements, trends of convergence and divergence of business cycles are identified using correlation analysis. Particularly, actual cross correlation and historical correlation in separated subsequent periods is applied in the analysis. Also an original measure of the European business cycle emergence was applied. The results do not provide an evidence of emerging European business cycle contrary to US cycle. The global economic crises was identified as a kind of negative symmetric shock pushing all major economies towards the recession phase of the cycle und thus increasing similarity. The results also shed some light on an influence of different detrending techniques when dissecting the cycles from the input macroeconomic time series.

PurposeQatar, a wealthy country with an open economy has limited arable land. To meet its domestic food demand, the country heavily relies on food imports. Additionally, the over three year-long economic embargo enforced by regional neighbors and the covariate shock of the COVID-19 pandemic have demonstrated the country's vulnerability to food insecurity and potential for structural breaks in macroeconomic data. The purpose of this paper is to examine short- and long-run determinants of Qatar's imports of aggregate food, meats, dairy and cereals in the presence of structural breaks.Design/methodology/approachThe authors use 24 years of food imports, gross domestic product (GDP) and consumer price index (CPI) data obtained from Qatar's Planning and Statistics Authority. They use the autoregressive distributed lag (ARDL) cointegration framework and Chambers and Pope's exact nonlinear aggregation approach.FindingsUnit root tests in the presence of structural breaks reveal a mixture of I (1) and I (0) variables for which standard cointegration techniques do not apply. The authors found evidence of a significant long-run relationship between structural changes and food imports in Qatar. Impulse response functions indicate full adjustments within three-quarters of a year in the event of an exogenous shock to imports.Research limitations/implicationsAn exogenous shock of one standard deviation on this variable would reduce Qatar's food imports by about 2.5% during the first period but recover after the third period.Originality/valueThe failure of past aggregate food demand studies to go beyond standard unit root testing creates considerable doubt about the accuracy of their elasticity estimates. The authors avoid that to provide more credible findings.