Innovational Outlier Research Articles

An Efficient Deep Learning-Based Troposphere ZTD Dataset Generation Method for Massive GNSS CORS Stations

Nowadays, a huge amount of GNSS continuously operating reference stations (CORS) have been established around the world, which have already been and will continue providing massive troposphere zenith total delay (ZTD) data. This paper proposes an efficient deep learning-based troposphere ZTD dataset generation method including ZTD series segmentation, addictive and innovational outlier detection, and missing data imputation. The overall standard deviation of first-order ZTD difference series between adjacent epochs of the selected CORS station in January 2018 is reduced from 0.84 to 0.26 mm with the 3-sigma rule and the wavelet decomposition strategy for outlier elimination. A dense neural network (DNN) is subsequently designed to impute missing ZTD data. Only 3.4 minutes are required for the DNN training using a NVIDIA GeForce RTX 3090Ti GPU. The complete ZTD series with missing ZTD data imputed by the well-trained DNN model has a good agreement with the ZTD series before the data imputation in terms of mean value (-0.0184 vs -0.0187 mm) and standard deviation (5.43 vs 5.26 mm). Complete ZTD series of 120 CORS stations are generated to further evaluate the computational efficiency of the proposed method. An average of 2.56/5.38/5.77/4.33 hours are necessary to generate the ZTD dataset for January/April/July/October in 2018, respectively. Our study confirms that the proposed method can efficiently generate CORS-based ZTD dataset, which could be extended to applications including troposphere temporal-spatial pattern exploration and ZTD augmentation on high-precision GNSS positioning.

Impact of Covid-19 on the Performance of The Nigeria`s Stock Market

This study identifies the structural break date in the series of All Share Index (ASI) of the Nigeria’s capital market using innovational outlier methodology with the Augmented Dickey-Fuller unit root with structural break test. The study also examines the descriptive characteristics and model structure of ASI before and after the identified break date using ARIMA methodology. It uses daily data of ASI from November 27, 2018 to November 24, 2020. The results indicate that the break date is March 6, 2020. The mean results decreased after the break. The series before the break follows ARIMA (3,1,12), while it follows ARIMA (7,1,9) after the break. The diagnostic test revealed that the ARIMA (7,1,9) fails to capture the entire variation in the series. The modified model for post break period is AR(7), MA(8) and MA(9) process. However, the estimated volatility of the series decreased after the break. The study recommends that capital market studies and policies going forward should incorporate the impact of Covid-19 induced structural break.

The effect of international energy prices on energy production in Sichuan, China

Sichuan Province is China’s leading natural gas and hydropower producer. This article tests for the effects of international energy (nominal) prices on natural gas and hydropower production in Sichuan. Monthly data cover the period from April 2002 to June 2019. This study conducts unit root tests using the standard augmented Dickey–Fuller (ADF) test, the Phillips–Perron (PP) test, and the Dickey–Fuller generalized least squared (GLS) test suggested by Elliott, Rothenberg and Stock (ERS), and the Perron break date innovational outlier (IO) Model C. It tests for long-run equilibrium using the Johansen multivariate method and Phillips–Ouliaris technique. It tests for weak exogeneity and estimates error-correction models (ECMs) and vector-autoregressive models (VARs). Overall, in the long run, both international spot and futures gas prices slightly and positively impacted the production of gas and hydropower. Differences between the spot and futures gas price effects were minor. International crude oil prices had insignificant effects on energy production. Energy production was gas price-inelastic. Long-run spot and futures gas price elasticities of gas output were 0.192 and 0.186, respectively. Given the strong governmental support for energy prices, Sichuan’s gas market has partially integrated into the global gas market. We suggest that, in the long run, both international futures and spot gas prices can be considered as an exogenous variable predicting changes in gas production. International futures gas prices can be a short-run factor predicting gas production. Gas production appears to serve as a long-run substitute for hydropower production; accordingly, with the growing gas supply, hydropower oversupply in Sichuan may become increasingly severe in the long run.

The Impact of Outliers on Parameter Estimation Method for Bilinear Model

Nonlinear least squares (NLS) method along with Newton-Raphson (NR) iterative procedure is the best method to estimate parameters for bilinear model. However, the existence of outliers will affect the estimated value of the parameter and its validity can be doubtful. This statement was proven by conducting simulation analysis for the bilinear model, especially on bilinear (1,0,1,1) model without and with the existence of additive outlier (AO), innovational outlier (IO), temporary change (TC) and level change (LC) in the data. The performance of the NLS method is measured in terms of bias. Numerical results show that, in general, the NLS method performs better in estimating the parameters without the existence of AO, IO, TC or LC in the data. Keywords: bilinear model; nonlinear least squares; Newton-Raphson; additive outlier; innovational outlier; temporary change; level change

An improved methodology for outlier detection in dynamic datasets

A time series Kalman filter (TSKF) is proposed that successfully handles outlier detection in dynamic systems, where normal process changes often mask the existence of outliers. The TSKF method combines a time series model fitting procedure with a modified Kalman filter to deal with additive outlier and innovational outlier detection problems in dynamic process dataset. Compared with current outlier detection methods, the new method enjoys the following advantages: (a) no prior knowledge of the process model is needed; (b) it is easy to tune; (c) it can be applied to both univariate and multivariate outlier detection; (d) it is applicable to both on‐line and off‐line operation; (e) it cleans outliers while maintains the integrity of the original dataset. © 2014 American Institute of Chemical Engineers AIChE J, 61: 419–433, 2015

Time Series Outlier Analysis of Tea Price Data

In this article Autoregressive Integrated Moving Average (ARIMA) models were fitted and outliers are identified for the auction price of tea in three regions- North India, South India and All India. The ARIMA models with seasonal differencing are found to be quite appropriate for the data. The region specific dynamics are distinctly assessed based on the autocorrelation functions. Further we are concerned with outliers in time series with two special cases, additive outlier (AO) and innovational outlier (IO).These outliers have been detected using two recent methods and conclusions drawn based on the data pertaining to the three regions. The reason for these types of outliers in the tea price have been further identified pointing towards the factors of environmental, weather conditions, pest attacks etc.

On the asymptotic distribution of a simple unit root test for trending and breaking series

In this paper, we derive the asymptotic distribution of Popp's (2008) innovational outlier unit root test for trending series with a break. The results of Zivot and Andrews (1992) are applied to provide the limiting results of these new test statistics. We tabulate their asymptotic and finite sample critical values, and illustrate the use of the new statistics with an application to the unemployment rate series for 23 OECD countries.

Bootstrap innovational outlier unit root tests in dependent panels

In this paper, we propose new simple innovational outlier (IO) panel unit root tests with a break. A bootstrap method for dealing with cross-sectional dependence is provided and small sample properties of the bootstrap tests are investigated by Monte Carlo experiments. The panel innovational outlier unit tests are then applied to a panel of 22 OECD inflation rates.

A note on the asymptotic distribution of a Perron-type innovational outlier unit root test with a break

This note provides the asymptotic distribution of a Perron-type innovational outlier unit root test developed by Popp (J Stat Comput Sim 78:1145–1161, 2008) in case of a shift in the intercept for non-trending data. In Popp (J Stat Comput Sim 78:1145–1161, 2008), only critical values for finite samples based on Monte Carlo techniques are tabulated. Using similar arguments as in Zivot and Andrews (J Bus Econ Stat 10:251–270, 1992), weak convergence is shown for the test statistics.

New innovational outlier unit root test with a break at an unknown time

The Perron test which is based on a Dickey–Fuller test regression is a commonly employed approach to test for a unit root in the presence of a structural break of unknown timing. In the case of an innovational outlier (IO), the Perron test tends to exhibit spurious rejections in finite samples when the break occurs under the null hypothesis. In the present paper, a new Perron-type IO unit root test is developed. It is shown in Monte Carlo experiments that the new test does not over-reject the null hypothesis. Even for the case of a level and slope break for trending data, the empirical size is near its nominal level. The test distribution equals the case of a known break date. Furthermore, the test is able to identify the true break date very accurately even for small breaks. As an application serves the Nelson–Plosser data set.

Modified seasonal unit root test with seasonal level shifts at unknown time

A modified innovational outlier seasonal unit root test for non-trending quarterly data is developed which accounts for seasonal level shifts at an unknown time. The superior test properties regarding size and break date estimation accuracy of the modified approach in contrast to the conventionally used procedures are derived by Monte Carlo analysis.

Detection Procedure for a Single Additive Outlier and Innovational Outlier in a Bilinear Model

A single outlier detection procedure for data generated from BL(1,1,1,1) models is developed. It is carried out in three stages. Firstly, the measure of impact of an IO and AO denoted by IO ω , AO ω , respectively are derived based on least squares method. Secondly, test statistics and test criteria are defined for classifying an observation as an outlier of its respective type. Finally, a general single outlier detection procedure is presented to distinguish a particular type of outlier at a time point t.

Savings, Investment and Growth in India

This article considers savings, investment and economic growth for India using annual time series data for the period 1950/51 to 2003/04. The analysis uses Perron's innovational outlier model to conduct unit root tests which endogenously determines structural break. The empirical results show that the null hypothesis of unit root cannot be rejected for gross domestic product. Moreover, the results show that the most significant structural breaks over the last five decades correspond to the wars, regime change and the nationalization of the banks. The study also utilizes the autoregressive distributed lag (ARDL) approach to test for cointegration. Whilst the results support the existing evidence for the Carroll-Weil hypothesis, the study also finds that saving unambiguously determines investment in both the short and long runs. No evidence is found to support the commonly accepted growth models in India, that investment is the engine of economic growth.

Residual‐based block bootstrap unit root testing in the presence of trend breaks

In this paper, we build on the ‘residual‐based block bootstrap unit root testing’ (RBB) method, proposed by Paparoditis and Politis (2003). We develop an extension of this method to allow for bootstrap unit root testing in a model defined by an augmented Dickey–Fuller (ADF) equation that contains linear combinations of arbitrary dummies as its deterministic part. The main application of such an extension is that it allows for unit root testing in the presence of arbitrary multiple trend breaks, such as jumps or changes of the slope of a linear trend. The model framework used here is an extension of Perron's ‘innovational outlier model’, and allows as well for gradual transitions of the expectation of the series when such breaks or outliers occur; this assumption is particularly appealing in the context of analysing economic time series. Our extension of the bootstrap method involves specifying a drift term and adjustments for the expectation of the residuals and the pseudo‐differences, which all appropriately take into account the dependency structure. We prove asymptotic validity of the proposed modified bootstrap procedure in the case of a single break in slope. The small sample behaviour of the proposed methodology is studied in a simulation experiment.

The impact of financial deregulation on monetary aggregates and interest rates in Australia

This study employs all quarterly time series currently available to endogenously determine the timing of structural breaks for various monetary aggregates and interest rates in Australia over the last 30 years. The Innovational Outlier model (IO) and the Additive Outlier model (AO) are then used to test for nonstationarity. After accounting for the single most significant structural break, the results from both models clearly indicate that the null of at least one unit root cannot be rejected for almost all series examined. The structural breaks found coincide with important policy changes during the period of financial deregulation starting in the 1980s.

Using Neural Networks to Detect and Classify Out-of-control Signals in Autocorrelated Processes

This paper presents an artificial neural network model for detecting and classifying three types of non-random disturbances referred to as level shift, additive outlier and innovational outlier which are common in autocorrelated processes. To the best of our knowledge, this is the first time that a neural network has been considered for simultaneous detection and classification of such non-random disturbances. An AR (1) model is considered to characterize the quality characteristic of interest in a continuous process where autocorrelated observations are generated over time. The performance of the proposed procedure is evaluated through the use of a numerical example. Preliminary results indicate that the procedure can be used effectively to detect and classify unusual shocks in autocorrelated processes. Copyright © 2003 John Wiley & Sons, Ltd.

Seasonal unit root tests with seasonal mean shifts

This paper analyses additive outlier and innovational outlier tests for seasonal unit roots when seasonal mean shifts occur under the null hypothesis. When the magnitude of the breaks is large, simulation evidence reveals that, for three of the four testing procedures considered, the endogenously determined break point can be incorrectly estimated, resulting in spurious rejections of the null. A simple modification to one of the testing approaches is proposed which achieves a substantial improvement in test size.

Innovational Outlier Unit Root Tests With an Endogenously Determined Break in Level

We show that a standard unit root test that permits an endogenously determined break in level can generate spurious rejections in practically interesting sample sizes when a large break occurs under the null hypothesis. This problem, which occurs for breaks of the innovational outlier type, can be corrected through a simple modification of the test procedure.

Stationarity and structural breaks — evidence from classical and Bayesian approaches

The purpose of this paper is to analyze and compare the results of applying classical and Bayesian methods to testing for a unit root in time series with a single endogenous structural break. We utilize a data set of macroeconomic time series for the Mexican economy similar to the Nelson–Plosser one. Under both approaches, we make use of innovational outlier models allowing for an unknown break in the trend function. Classical inference relies on bootstrapped critical values, in order to make inference comparable to the finite sample Bayesian one. Results from both approaches are discussed and compared.

Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time

The authors consider unit root tests that allow a shift in trend at an unknown time. They focus on the additive outlier approach but also give results for the innovational outlier approach. Various methods of choosing the break date are considered. New limiting distributions are derived, including the case where a shift in trend occurs under the unit root null hypothesis. Limiting distributions are invariant to mean shifts but not to slope shifts. Simulations are used to assess finite sample size and power. The authors focus on the effects of a break under the null and the choice of break date. Copyright 1998 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.