Most recent changepoint detection in Panel data

Detecting recent changepoints in time-series can be important for short-term prediction, as we can then base predictions just on the data since the changepoint. In many applications we have panel data, consisting of many related univariate time-series. We present a novel approach to detect sets of most recent changepoints in such panel data which aims to pool information across time-series, so that we preferentially infer a most recent change at the same time-point in multiple series. Our approach is computationally efficient as it involves analysing each time-series independently to obtain a profile likelihood like quantity that summarises the evidence for the series having either no change or a specific value for its most recent changepoint. We then post-process this output from each time-series to obtain a potentially small set of times for the most recent changepoints, and, for each time, the set of series which has their most recent changepoint at that time. We demonstrate the usefulness of this method on two data sets: forecasting events in a telecommunications network and inference about changes in the net asset ratio for a panel of US firms

Change Point Estimation in Panel Data with Time-Varying Individual Effects

This paper proposes a method for estimating multiple change points in panel data models with unobserved individual effects via ordinary least-squares (OLS). Typically, in this setting, the OLS slope estimators are inconsistent due to the unobserved individual effects bias. As a consequence, existing methods remove the individual effects before change point estimation through data transformations such as first-differencing. We prove that under reasonable assumptions, the unobserved individual effects bias has no impact on the consistent estimation of change points. Our simulations show that since our method does not remove any variation in the dataset before change point estimation, it performs better in small samples compared to first-differencing methods. We focus on short panels because they are commonly used in practice, and allow for the unobserved individual effects to vary over time. Our method is illustrated via two applications: the environmental Kuznets curve and the U.S. house price expectations after the financial crisis.Comment: 26 page

Beyond Cumulative Sum Charting in Non-Stationarity Detection and Estimation

In computer science, stochastic processes, and industrial engineering, stationarity is often taken to imply a stable, predictable flow of events and non-stationarity, consequently, a departure from such a flow. Efficient detection and accurate estimation of non-stationarity are crucial in understanding the evolution of the governing dynamics. Pragmatic considerations include protecting human lives and property in the context of devastating processes such as earthquakes or hurricanes. Cumulative Sum (CUSUM) charting, the prevalent technique to weed out such non-stationarities, suffers from assumptions on a priori knowledge of the pre and post-change process parameters and constructs such as time discretization. In this paper, we have proposed two new ways in which non-stationarity may enter an evolving system - an easily detectable way, which we term strong corruption, where the post-change probability distribution is deterministically governed, and an imperceptible way which we term hard detection, where the post-change distribution is a probabilistic mixture of several densities. In addition, by combining the ordinary and switched trend of incoming observations, we develop a new trend ratio statistic in order to detect whether a stationary environment has changed. Surveying a variety of distance metrics, we examine several parametric and non-parametric options in addition to the established CUSUM and find that the trend ratio statistic performs better under the especially difficult scenarios of hard detection. Simulations (both from deterministic and mixed inter-event time densities), sensitivity-specificity type analyses, and estimated time of change distributions enable us to track the ideal detection candidate under various non-stationarities. Applications on two real data sets sampled from volcanology and weather science demonstrate how the estimated change points are in agreement with those obtained in some of our previous works, using different methods. Incidentally, this study sheds light on the inverse nature of dependence between the Hawaiian volcanoes Kilauea and Mauna Loa and demonstrates how inhabitants of the now-restless Kilauea may be relocated to Mauna Loa to minimize the loss of lives and moving costs

Efficient search methods for high dimensional time-series

This thesis looks at developing efficient methodology for analysing high dimensional time-series, with an aim of detecting structural changes in the properties of the time series that may affect only a subset of dimensions. Firstly, we develop a Bayesian approach to analysing multiple time-series with the aim of detecting abnormal regions. These are regions where the properties of the data change from some normal or baseline behaviour. We allow for the possibility that such changes will only be present in a, potentially small, subset of the time-series. A motivating application for this problem comes from detecting copy number variation (CNVs) in genetics, using data from multiple individuals. Secondly, we present a novel approach to detect sets of most recent changepoints in panel data which aims to pool information across time-series, so that we preferentially infer a most recent change at the same time point in multiple series. Lastly, an approach to fit a sequence of piece-wise linear segments to a univariate time series is considered. Two additional constraints on the resulting segmentation are imposed which are practically useful: (i) we require that the segmentation is robust to the presence of outliers; (ii) that there is an enforcement of continuity between the linear segments at the changepoint locations. These constraints add significantly to the computational complexity of the resulting recursive solution. Several steps are investigated to reduce the computational burden