Moving Sums Research Articles

The empirical analysis of the two types of change points estimation algorithms based on MOSUM

Abstract In order to make big data play a greater value in financial markets, exploring a new data processing method to improve the ability to detect structural mutations is necessary for the diagnosis and monitoring of financial data and investment direction. This article applies financial time series data, based on the moving sum (MOSUM) statistics, empirically analyzes changes of stock data in Kweichow Moutai in the past ten years. Detecting the feasibility of two multiscale MOSUM algorithms of bottom-up merging and local pruning and visualizing the results by numerical simulation, combined with the fact of the time point, we proved the consistent advantages of the two algorithms in detecting the accuracy and precision of variable points.

Inference of Breakpoints in High-dimensional Time Series

For multiple change-points detection of high-dimensional time series, we provide asymptotic theory concerning the consistency and the asymptotic distribution of the breakpoint statistics and estimated break sizes. The theory backs up a simple two-step procedure for detecting and estimating multiple change-points. The proposed two-step procedure involves the maximum of a MOSUM (moving sum) type statistics in the first step and a CUSUM (cumulative sum) refinement step on an aggregated time series in the second step. Thus, for a fixed time-point, we can capture both the biggest break across different coordinates and aggregating simultaneous breaks over multiple coordinates. Extending the existing high-dimensional Gaussian approximation theorem to dependent data with jumps, the theory allows us to characterize the size and power of our multiple change-point test asymptotically. Moreover, we can make inferences on the breakpoints estimates when the break sizes are small. Our theoretical setup incorporates both weak temporal and strong or weak cross-sectional dependence and is suitable for heavy-tailed innovations. A robust long-run covariance matrix estimation is proposed, which can be of independent interest. An application on detecting structural changes of the U.S. unemployment rate is considered to illustrate the usefulness of our method.

A monitoring procedure for detecting structural breaks in factor copula models

Abstract We propose a new monitoring procedure based on moving sums (MOSUM) for detecting single or multiple structural breaks in factor copula models. The test compares parameter estimates from a rolling window to those from a historical data set and analyzes the behavior under the null hypothesis of no parameter change. The case of multiple breaks is also treated. In the model, the joint copula is given by the copula of random variables which arise from a factor model. This is particularly useful for analyzing high dimensional data. Parameters are estimated with the simulated method of moments (SMM). We analyze the behavior of the monitoring procedure in Monte Carlo simulations and a real data application. We consider an online procedure for predicting the day-ahead Value-at-risk based on the suggested monitoring procedure.

Power of the MOSUM test for online detection of a transient change in mean

In this article we discuss an online moving sum (MOSUM) test for detection of a transient change in the mean of a sequence of independent and identically distributed (i.i.d.) normal random variables. By using a well-developed theory for continuous time Gaussian processes and subsequently correcting the results for discrete time, we provide accurate approximations for the average run length (ARL) and power of the test. We check theoretical results against simulations, compare the power of the MOSUM test with that of the cumulative sum (CUSUM), and briefly consider the cases of nonnormal random variables and weighted sums.

Asymptotic modelling of corn plant data using moving sums (MOSUM) technique

Empirical model building using linear regression has been widely used in agricultural study. The validity of an assumed model is usually check using either F of likelihood ratio test under normally distributed observations. In this paper an asymptotic method based on the moving sums (MOSUM) of triangular array of ordinary least squares (OLS) residuals is proposed. Reasonable tests statistics for detecting valid model are defined as the Kolmogorov-Smirnov (KS) and Cramér-von Mises (MvM) functionals of the residual MOSUM process. The limit process is obtained for the condition under H0 and under H1 by applying the continuous mapping theorem to the existing limit theorem for partial sums of the residuals. The quantiles of the KS and CvM statistics under H0 are approximated by simulation. The application of the method in obtaining a valid model for the speed of growth of corn plants results in the conclusion that a first-order polynomial regression model is shown to be plausible.

Power behavior of test based on the moving sums (MOSUM) of spatial least squares residuals

The optimality of a test can be studied by investigating the behavior of the corresponding power function under alternatives. In this paper we study the rate of decay of power functions obtained from asymptotic model validity tests in linear regression analysis based on the moving sums (MOSUM) process of ordinary least squares (OLS) residuals of univariate spatial observations. The powers under study appear as the evaluation of the probability of events generated by the Kolmogorov-Smirnov (KS) and Cramer-von Mises functionals of the Slepian field plus a deterministic trend. It is shown under mild conditions that the rate of the power to the size of test is bounded by a constant which is proportional to the length of the trend. It is also shown that the rate of decays of the powers of the KS and CvM MOSUM tests coincide with the Neyman-Pearson test which is most powerful (MP) test for simple hypotheses. The performance of the power functions are also discussed by simulation.

Services sector and economic growth in India

This study examines the long-run equilibrium and short-run dynamic relationship between services sector and Gross Domestic Product (GDP) and between services and nonservices sectors in India. The model is estimated using the optimal single-equation and the maximum-likelihood system estimators. All the estimators consistently suggest the cointegrating relationship between services sector and GDP as well as between services and nonservices sectors. The estimates of long-run elasticity parameters are statistically significant and dimensionally consistent across the estimators. The conventional Cumulative Sum (CUSUM) and the new CUSUM and Moving Sum (MOSUM) tests suggest the stability of the equilibrium residuals and reinforce the cointegrating relationship between the model series. The error correction model provides some support for unidirectional Granger-causality from services sector to GDP. The impulse response and variance decomposition analyses instead suggest the bidirectional causality between services sector and GDP and between services and nonservices sectors. The stable growth of services sector is essentially crucial to absorb the adverse effects of exogenous weather shocks in agriculture and industry and provide resilience to the economy.

Monitoring Structural Changes in Generalized Linear Models

In this article, we introduce two monitoring schemes to (sequentially) detect structural changes in generalized linear models and develop asymptotic theories for them. The first method is based on cumulative sums (CUSUM) of weighted residuals, in which the unknown in-control parameters have been replaced by its maximum likelihood (ML) estimate from the training sample, whereas the second scheme makes use of moving sums (MOSUM) of weighted residuals. We characterize the limit distribution of the test statistic and show that these tests are consistent. Moreover, we also obtain and tabulate the asymptotic critical values of the tests. Finally, we study the speed of detection under different conditions. The methods are illustrated and compared in several simulations.

Applications of permutations to the simulations of critical values

Permuting the observations can provide an approximation for the distribution function of our test statistic. We show that invariance principles provide rates of convergence for the simulation. Bounds for the rate of convergence of cumulative sum (CUSUM), moving sum (MOSUM) and maximally selected (weighted) CUSUM statistics are examples for our method.

The Use of MOSUMS for Quality Control

The use of moving sums (MOSUMS) of recursively calculated residuals (Hack1 [9]) is demonstrated for testing the constancy of the expected value of a series of T independent observations normally distributed with equal variances. The cases of known or unknown expected value are treated separately; in the situation of unknown variance the recursive estimation of the variance is suggested in the course of the sequential application of the test procedure. Conservative probability limits are constructed and an assessment of the effective error probabilities and the power of the method is given in simulation studies. Finally the use of the procedure is demonstrated in an example.