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The paper explores the characteristics associated with the formation of bubbles that occurred in the Hong Kong stock market in 1997 and 2007, as well as the 2000 dot-com bubble of Nasdaq. It examines the profitability of technical analysis ( TA ) strategies generating buy and sell signals, with and without our proposed trading rules. The empirical results show that, by applying long and short strategies during the bubble formation and a short strategy after the bubble burst, it not only produces returns that are significantly greater than buy-and-hold strategies, but also produces greater wealth compared with TA strategies without trading rules. We conclude that these bubble detection signals help investors generate greater wealth from applying appropriate long and short moving average ( MA ) strategies.

A problem of interest in economic and finance applications is testing whether ARMA (Autoregressive moving average) errors are uncorrelated under weak assumptions, namely assumptions where the errors are neither iid nor a martingale difference. In this paper, non-standard versions of the tests of serial correlation introduced by Andrews and Ploberger (1996, hereafter AP) are proposed for diagnostic checking of ARMA errors. The original AP tests are designed for the case where the observed time series is generated by ARMA(1,1) models under the alternative and use asymptotic critical values computed by AP. The non-standard testing procedure uses AP statistics calculated from residuals and critical values based on asymptotic distribution theory derived under weak assumptions. The motivation for modifying the original AP tests is that they have attractive properties for the case for which they were originally designed: They are consistent against all non-white noise alternatives and have good all-round power against non-seasonal alternatives compared to several widely used tests in the literature, including those of Box and Pierce (1970, hereafter BP) and Ljung and Box (1978, hereafter LB) tests. A further advantage of the AP tests is that there is no need to specify a cutoff lag-length as is necessary for the BP and LB tests. We compare the non-standard AP tests with the non-standard BP and LB tests proposed by Francq et al. (2005), the tests of Hong and Lee (2007), and the tests using standardized residuals proposed by Chen (2008). In Monte Carlo experiments using ARMA models with GARCH (Generalised autoregressive conditional heteroskedasticity), EGARCH (Exponential GARCH) and non-MDS (Martingale difference sequence) innovations, the non-standard AP tests generally have better power than the other tests we consider. This suggests that the power advantage of the original AP tests extends to the more general framework considered in this paper.

This paper reinforces the previously proposed moving linear (ML) model approach for time series analysis by introducing theoretically grounded enhancements. The ML model flexibly decomposes a time series into constrained and remaining components, enabling the extraction of trends and fluctuations with minimal structural assumptions. Building on this framework, we present two key improvements. First, we develop a theoretically justified evaluation criterion that facilitates coherent estimation of model parameters, particularly the width of the time interval. Second, we enhance the extended ML (EML) model by introducing a new outlier detection and estimation method that identifies both the number and locations of outliers by maximizing the reduction in AIC. Unlike the earlier version, the reinforced EML model simultaneously estimates outlier effects and improves model fit within a unified, likelihood-based framework. Empirical applications to economic time series illustrate the method’s superior ability to detect meaningful anomalies and produce stable, interpretable decompositions. These contributions offer a generalizable and theoretically supported approach to modeling nonstationary time series with structural disturbances.

This study presents an innovative approach for detecting and estimating outliers in time series data, emphasizing constrained-remaining components decomposition. The method extends the moving linear model to accommodate outliers, resulting in an enhanced moving linear model. A state-space representation improves computational efficiency through Bayesian estimation. We introduce a novel method for determining outlier positions, starting with initial estimates of the remaining components. The proposed methodology combines maximum likelihood and Bayesian-type estimation for effective outlier detection and estimation, guided by the minimum Akaike Information Criterion (AIC). Furthermore, we investigate outlier detection in time series data with seasonal components. Applications to real data, specifically the Index of Industrial Production (IIP) and Wholesale Commercial Sales (WCS) in Japan, showcase the simplicity and potential for automation in the proposed approach, making it a promising tool for time series analysis, particularly in constrained-remaining components decomposition.

Wholesale sales value is one of the key elements included in the coincident indicator series of the indexes of business conditions in Japan. The objectives of this study are twofold. The first is to comprehend features of dynamic structure of various components for 12 business types of the wholesale sales in Japan, focusing on the period from January 1980 to December 2022. The second is to elucidate effect of business cycles on the behavior of each business type of wholesale sales. Specifically, we utilize our moving linear model approach to decompose monthly time-series data of wholesale sales into a seasonal component, an unusually varying component containing outliers, a constrained component, and a remaining component. Additionally, we construct a distribution-free dynamic linear model and examine the time-varying relationship between the decomposed remaining component, which contains cyclical variation, in each business type of the wholesale sales and that in the coincident composite index. Our proposed approach reveals complex dynamics of various components of time series on wholesale sales. Furthermore, we find that different business types of the wholesale sales exhibit diverse responses to business cycles, which are influenced by macroeconomic conditions, government policies, or exogenous shocks.

We propose a methodology for decomposing time series data into multiple components, including constrained components and remaining components containing cyclical variation. Our approach employs a moving linear model and utilizes state space representation, allowing for estimation of the components using the Kalman filter. The key parameter in our model is the width of the time interval, which can be estimated using the maximum likelihood method. Notably, our approach only requires a local linear model for the constrained component, while a strict model is not necessary for the remaining component. By applying our approach iteratively, we can decompose a time series into multiple components. Furthermore, we introduce a procedure to transform the decomposed components into uncorrelated components using principal component analysis. The proposed methodology demonstrates its applicability in analyzing business cycles. To illustrate its performance, we apply it to analyze two sets of monthly time series data from Japan.

One of the most popular univariate asymmetric conditional volatility models is the exponential GARCH (or EGARCH) specification. In addition to asymmetry, which captures the different effects on conditional volatility of positive and negative effects of equal magnitude, EGARCH can also accommodate leverage, which is the negative correlation between returns shocks and subsequent shocks to volatility. However, the statistical properties of the (quasi-) maximum likelihood estimator of the EGARCH parameters are not available under general conditions, but rather only for special cases under highly restrictive and unverifiable conditions. It is often argued heuristically that the reason for the lack of general statistical properties arises from the presence in the model of an absolute value of a function of the parameters, which does not permit analytical derivatives, and hence does not permit (quasi-) maximum likelihood estimation. It is shown in this paper for the non-leverage case that: (1) the EGARCH model can be derived from a random coefficient complex nonlinear moving average (RCCNMA) process; and (2) the reason for the lack of statistical properties of the estimators of EGARCH under general conditions is that the stationarity and invertibility conditions for the RCCNMA process are not known.

Abstract—The article describes the computations of purchasing power parities and proposes to use the moving linear segment procedure in order to assess the stratification of the aggregate of the EU/OECD–CIS economies. The results of calculations on PPP-based identification of low-, middle- and high-income groups are presented. The trend of several macroeconomic indicators for changing with an increase in per capita GDP is shown to be shaped similarly to the logistic curve. According to the results, the Russian economy belongs to the middle income group.

In this paper, a measurement system for roll error (angular error of a linear moving stage) is described. The proposed system consists of four capacitance sensors located at four vertices of a tetragon in a fixture. Unnecessary measured data due to global surface roughness on the measuring target is eliminated using a differential method. First, a mathematical model for the proposed system is developed using the error synthesis modeling technique. The zero adjustment difference is a critical parameter for precise measurement. Therefore, an additional measurement procedure is developed to estimate the zero adjustment difference. The x - and y -directional offset errors, which are deviation from the designed position of hole for holding a capacitance sensor, introduce an error in the estimation of roll error. Therefore, a virtual experiment is performed with different values of x - and y -directional offset error to analyze their effect. Then, the roll error is measured using the proposed measurement system. A comparison of the measured data from the proposed method (four capacitance sensors) and the conventional method (two capacitance sensors and a straight-edge) is performed. Finally, the proposed method is verified using a hypothesis test.

It is desirable to operate linear compressors close to their natural frequency with the help of a mechanical spring. By this way, the required current values are kept to a minimum while obtaining a smooth oscillation. On the other hand, the force applied by the compressed gas on the piston varies nonlinearly depending on the compressor’s compression ratio and gas flow rate. This affects the natural frequency of the oscillation. In this study, it is aimed to examine the effect of the change in the operating frequency on the electrical characteristics and efficiency of the motor. For this purpose, the linear compressor is modeled with the lumped parameter approach. Structural electrical properties of the compressor such as winding resistance, inductance and motor emf constant were taken from a sample compressor and kept at constant value. In the simulation studies, the electrical behavior of the motor and the dynamic behavior of the piston were examined by feeding the system with voltage at different frequencies and amplitudes for different pressure ratios and compressor capacities. For each operating condition, the electrical efficiency of the motor was calculated, and the variation of magnetic force, current and voltage was determined. The results show that the operating frequency strongly affects the maximum voltage and current values, and the appropriate frequency changes with the pressure and capacity. The study reveals that adjusting the operating frequency can enhance efficiency by up to 10% under low-pressure rates and partial loads.