Decline in Temperature Variability on Svalbard

AbstractThe variability in the temperature on Svalbard, Norway, has been decreasing over the last four decades. This may be due to the reduction in sea ice, transitioning the regional climate to a more stable, coastal one. We quantify this transition in terms of decreasing volatility in a daily average temperature time series at Svalbard Airport from 1976 to 2019. We use two different approaches: a nonstochastic model and a time-dependent generalized autoregressive conditional heteroskedasticity (GARCH) model. These parametric approaches include a time-dependent trend, where the slope depends on the day of the year. For Svalbard, the slope has a minimum in late August and the steepest slope during winter is estimated to be −0.1°C2 yr−1. The nonstochastic model, for which the conditional and unconditional variances are the same, only depends on the marginal distribution and is perhaps the easiest to interpret. The GARCH model extends the nonstochastic model by including short-range temporal dependence in the volatility and is thus more locally adapted. Volatility modeling is important for a complete statistical description of the temperature dynamics on Svalbard as an Arctic representative. In combination with increasing temperatures, the volatility reduction makes the extremely cold days during winter occur less frequently. Although we focus exclusively on the Svalbard Airport series, the models should be suitable for other temperature or climatic time series.

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A Novel Fuzzy Linear Regression Sliding Window GARCH Model for Time-Series Forecasting

Applied Sciences ◽

10.3390/app10061949 ◽

2020 ◽

Vol 10 (6) ◽

pp. 1949

Author(s):

Amiratul L. Mohamad Hanapi ◽

Mahmod Othman ◽

Rajalingam Sokkalingam ◽

Nazirah Ramli ◽

Abdullah Husin ◽

...

Keyword(s):

Time Series ◽

Linear Regression ◽

Garch Model ◽

Sliding Window ◽

Time Series Forecasting ◽

Likelihood Method ◽

Fuzzy Linear Regression ◽

Specific Distribution ◽

Proposed Model ◽

The Garch Model

Generalized autoregressive conditional heteroskedasticity (GARCH) is one of the most popular models for time-series forecasting. The GARCH model uses a maximum likelihood method for parameter estimation. For the likelihood method to work, there should be a known and specific distribution. However, due to uncertainties in time-series data, a specific distribution is indeterminable. The GARCH model is also unable to capture the influence of each variance in the observation because the calculation of the long-run average variance only considers the series in its entirety, hence the information on different effects of the variances in each observation is disregarded. Therefore, in this study, a novel forecasting model dubbed a fuzzy linear regression sliding window GARCH (FLR-FSWGARCH) model was proposed; a fuzzy linear regression was combined in GARCH to estimate parameters and a fuzzy sliding window variance was developed to estimate the weight of a forecast. The proposed model promotes consistency and symmetry in the parameter estimation and forecasting, which in turn increases the accuracy of forecasts. Two datasets were used for evaluation purposes and the result of the proposed model produced forecasts that were almost similar to the actual data and outperformed existing models. The proposed model was significantly fitted and reliable for time-series forecasting.

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Aplikasi GARCH dalam Mengatasi Volatilitas Pada Data Keuangan

Jurnal Matematika ◽

10.24843/jmat.2017.v07.i02.p87 ◽

2017 ◽

Vol 7 (2) ◽

pp. 107

Author(s):

, Hartati ◽

Imelda Saluza

Keyword(s):

Time Series ◽

Garch Model ◽

Practical Experience ◽

Financial Data ◽

Demand And Supply ◽

Volatility Clustering ◽

Wide Range ◽

One Year ◽

The Garch Model

The financial market is a place or means convergence between demand and supply of a wide range of financial instruments Long-term (over one year). Activities that occur in the financial markets in the long term will form a series of data is often called a time series that contains a set of information from time to time. Practical experience shows that many time series exhibit their periods with great volatility. The greater the volatility, the greater the chance to experience a gain or loss. Important properties are often owned by the data time series in finance, especially to return data that the probability distribution of returns are fat tails (tail fat) and volatility clustering or often referred to as a case heteroskedastisitas. Not all models are able to capture the nature of heteroscedasticity, one of the models that are able to do is Generalized Autoregressive Heteroskedasticity Condition (GARCH). So the purpose of this study was to determine the GARCH model in dealing with the volatility that occurred in the financial data. The results showed that the GARCH model is best suited to see volatility in the financial data.

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Multidimensional extremes: joint study of precipitation and temperature time series

10.5194/ems2021-223 ◽

2021 ◽

Author(s):

Beatrix Izsák ◽

Tamás Szentimrey ◽

Mónika Lakatos ◽

Rita Pongrácz

Keyword(s):

Climate Change ◽

Time Series ◽

Extreme Values ◽

Standardized Precipitation Index ◽

Single Element ◽

Average Temperature ◽

Temperature And Precipitation ◽

The Standardized Precipitation Index ◽

Climatic Time Series ◽

Precipitation And Temperature

<p>To study climate change, it is essential to analyze extremes as well. The study of extremes can be done on the one hand by examining the time series of extreme climatic events and on the other hand by examining the extremes of climatic time series. In the latter case, if we analyze a single element, the extreme is the maximum or minimum of the given time series. In the present study, we determine the extreme values of climatic time series by examining several meteorological elements together and thus determining the extremes. In general, the main difficulties are connected with the different probability distribution of the variables and the handling of the stochastic connection between them. The first issue can be solved by the standardization procedures, i.e. to transform the variables into standard normal ones. For example, the Standardized Precipitation Index (SPI) uses precipitation sums assuming gamma distribution, or the standardization of temperature series assumes normal distribution. In case of more variables, the problem of stochastic connection can be solved on the basis of the vector norm of the variables defined by their covariance matrix. According to this methodology we have developed a new index in order to examine the precipitation and temperature variables jointly. We present the new index with the mathematical background, furthermore some examples for spatio-temporal examination of these indices using our software MASH (Multiple Analysis of Series for Homogenization; Szentimrey) and MISH (Meteorological Interpolation based on Surface Homogenized Data Basis; Szentimrey, Bihari). For our study, we used the daily average temperature and precipitation time series in Hungary for the period 1870-2020. First of all, our analyses indicate that even though some years may not be considered extreme if only either precipitation or average temperature is taken in to account, but examining the two elements together these years were extreme years indeed. Based on these, therefore, the study of the extremes of multidimensional climate time series complements and thus makes the study of climate change more efficient compared to examining only one-dimensional time series.</p>

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Análise de dados climáticos usando transformada em ondeletas cruzada e coerência

Revista Brasileira de Geografia Física ◽

10.26848/rbgf.v13.2.p641-647 ◽

2020 ◽

Vol 13 (2) ◽

pp. 641

Author(s):

Roseilson Souza Vale ◽

Raoni Aquino Santana ◽

Cléo Queresma Dias Júnior

Keyword(s):

Time Series ◽

Air Temperature ◽

Wavelet Coherence ◽

Climate Data ◽

Mathematical Relationship ◽

Cross Wavelet Transform ◽

Climatic Time Series ◽

Wavelet Coherence Analysis ◽

Temperature Time ◽

Cross Wavelet

Este estudo mostra uma análise em transformada em ondeleta cruzada e coerência em ondeleta aplicada a duas séries temporais, sendo uma delas precipitação e a outra temperatura do ar. O objetivo deste estudo é mostrar que esta técnica é uma ferramenta poderosa na análise de séries temporais climáticas, para isso à aplicamos a duas séries com relação física muito conhecida na climatologia. Além da aplicação realizada, recorreu-se também a uma descrição matemática dos métodos. A técnica da transformada em ondeletas cruzada e coerência mostrou-se eficiente em capturar a relação matemática entre as séries de precipitação e temperatura do ar. Com este estudo esperamos difundir o uso desta técnica para fins de ensino e pesquisa em diversos sistemas geofísicos. Analysis of Climate Data Using Transformed Crosswave and Coherence A B S T R A C TThis study presents a cross wavelet transform and wavelet coherence analysis applied to a precipitation and an air temperature time series. The objective of this study is to demonstrate that this technique is a powerful tool in the analysis of climatic time series, and can be applied to two time series with very well-known physical relationships in terms of climatology. In addition to this application, a mathematical description of the methods was done. The cross-curves and coherence technique proved to be efficient in capturing the mathematical relationship between precipitation series and air temperature. With this study we hope to disseminate the use of this technique for teaching and research purposes in various geophysical systems.Keywords: Phase Angle, Wavelet Coherence, Cross wavelet, Precipitation, Temperature.

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Trend analysis using non-stationary time series clustering based on the finite element method

Nonlinear Processes in Geophysics ◽

10.5194/npg-21-605-2014 ◽

2014 ◽

Vol 21 (3) ◽

pp. 605-615 ◽

Cited By ~ 14

Author(s):

M. Gorji Sefidmazgi ◽

M. Sayemuzzaman ◽

A. Homaifar ◽

M. K. Jha ◽

S. Liess

Keyword(s):

Time Series ◽

Temperature Time Series ◽

Stationary Time Series ◽

Change Points ◽

The Finite Element Method ◽

Clustering Method ◽

Time Series Clustering ◽

Stationary Time ◽

Climatic Time Series ◽

Temperature Time

Abstract. In order to analyze low-frequency variability of climate, it is useful to model the climatic time series with multiple linear trends and locate the times of significant changes. In this paper, we have used non-stationary time series clustering to find change points in the trends. Clustering in a multi-dimensional non-stationary time series is challenging, since the problem is mathematically ill-posed. Clustering based on the finite element method (FEM) is one of the methods that can analyze multidimensional time series. One important attribute of this method is that it is not dependent on any statistical assumption and does not need local stationarity in the time series. In this paper, it is shown how the FEM-clustering method can be used to locate change points in the trend of temperature time series from in situ observations. This method is applied to the temperature time series of North Carolina (NC) and the results represent region-specific climate variability despite higher frequency harmonics in climatic time series. Next, we investigated the relationship between the climatic indices with the clusters/trends detected based on this clustering method. It appears that the natural variability of climate change in NC during 1950–2009 can be explained mostly by AMO and solar activity.

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The Assessment of Time Series for an Entire Air Quality Control District in Southern Taiwan Using GARCH Model

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i3.19.16999 ◽

2018 ◽

Vol 7 (3.19) ◽

pp. 119 ◽

Cited By ~ 1

Author(s):

Shu Lung Kuo ◽

Ching Lin Ho

Keyword(s):

Time Series ◽

Quality Control ◽

Air Quality ◽

Air Pollutants ◽

Garch Model ◽

Multiple Time ◽

Asymmetric Volatility ◽

Air Quality Control ◽

The Garch Model ◽

T Distribution

The General Autoregressive Conditional Heteroskedastic (GARCH) model and 10 ordinary air quality monitoring stations in the entire air quality control district in Kaohsiung-Pingtung were used in this study. First, the factor analysis results within multivariate statistics were employed to select the main factor that affects air pollution, namely, the photochemical pollution factor. The characteristics of the GARCH model were discussed in terms of asymmetric volatility among the three air pollutants (PM10, NO2, and O3) within the factor. In addition, this study also combined the multiple time series model VARMA to explore changes in the time series of the three air pollutants and to discuss their predictability.The results showed that, although the coefficient of the GARCH model was negative when estimating the variance equation, the conditional variance would always be positive after taking the logarithm. The results also suggested that the GARCH model was quite capable of capturing the asymmetric volatility. In other words, if the condition that pollution factors might be subject to seasonal changes or outliers generated by the human contamination is not considered, the GARCH model had very good ability to verify the results and make predictions, regardless of whether it adopted any of the three risk concepts: normal distribution, t-distribution, and generalized error distribution. For example, under the trend of time series temporal and spatial distribution in various pollution concentrations of photochemical factors, the optimal model VARMA(2,0,0)-GARCH(1,1) selected in this study was used to conduct time series predictability after the verification procedure. After capturing the last 50 entries of data on O3 concentrations in the sequence, the results showed that the predictability correlation (r) was 0.812, the predictability of NO2 was 0.783 and the predictability of PM10 was 0.759. It can be learned from the results that under the sequence of the GARCH model with strong asymmetric volatility, the residual values of these three sequences as white noise were quite evident, and there was also a high degree of correlation in predictability.

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