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

Boosting 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.

Power to Detect Spatial Disturbances under Different Levels of Geographic Aggregation

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.

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. 

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.

In business-cycle research, smoothing data is an essential first step to evaluate the extent to which model-generated moments stand up to their empirical counterparts. We put to test McDermott’s (1997) modified version of Hodrick and Prescott’s (1997) smoothing filter. On the one hand, our simulations suggest that relative to other filters, the modified HP-filter replicates better artificially generated series with known properties. On the other hand, using true data we find that autoregressive properties of smoothed series are not affected by the choice of smoothing HP filters, but the same does not hold when it comes to multivariate analysis. The later result is especially strong for annual data. We report results for a large set of countries.

The existence and magnitude of scale economies for firms has long been an important issue. Identifying and measuring the factors affecting scale relationships is, however, difficult since they encompass a wide range of interactions related to a broadly defined notion of Short run scale effects are due to substitution constrained by fixity of private capital; long run (internal) scale economies result from utilizing the technology embodied in existing capital more efficiently as production expands; and external scale effects arise from technological factors associated with industryor economy-wide capital accumulation, which increases input-effectiveness. A number of such external or shift factors have been identified in traditional productivity or endogenous growth models, most of which can be expressed in terms of an increase in the availability or effectiveness of either physical or human capital. These include regulations, public infrastructure, R&D, and changes in the composition and quality of the labour force and capital stock, in addition to the more generic notion of disembodied or exogenous technical change. A combination of these scale effects and internal scale economies drives observed fluctuations and growth of firms and industries. Untangling the complex interactions involved requires a model that explicitly incorporates the various scale factors. In this paper we begin to shed some light on these interactions and the resulting pattern of internal and external scale effects in U.S. manufacturing. First, we provide a theoretical structure that can be used to identify the external and internal effects embodied in observed cost-output relationships. We then apply this framework to data at different levels of aggregation -aggregating from the 4-digit manufacturing level to 2-digit and then to total manufacturing -to assess whether identifiable patterns or biases emerge in

This chapter departs from most studies of the gender use divide in the mobile Internet, in that it deals with the topic at different levels of aggregation, namely the global, the regions of the world, developing countries and intra-country. Broadly, the results accord with what one would expect, namely, that there is a bias against females in the use of the mobile Internet at the different levels (using the most recent data from international institutions that are concerned with the issue). But at lower levels of aggregation, there are cases where relatively poor countries perform much better than expected, or where cases can be found that are intended to, and are in some cases, successful in reducing the gender digital divide in mobile Internet use. Many of these are to be found in India and have already spread to other countries in the Global South. Overall, these examples support the view that a reduction in the gender divide requires much more attention than it has hitherto been granted.KeywordsGender digital use divideLevels of aggregationPoor countriesOutliersIndia