scholarly journals Statistical Analysis of New Zealand Electricity Prices: A Risk Manager's Perspective

2021 ◽  
Author(s):  
◽  
Caroline Moy
Keyword(s):  
Time Series ◽  
New Zealand ◽  
Price Volatility ◽  
Distribution Functions ◽  
Electricity Price ◽  
Cumulative Distribution ◽  
Electricity Prices ◽  
Sarima Model ◽  
Price Data ◽  
Risk Manager

<p>This thesis considers the conventional SARIMA model and the EVT-GARCH model for forecasting electricity prices. However, we find that these models do not adequately capture the important characteristics of the electricity price data. A new model is developed, the EVT-SARIMA model, for forecasting electricity prices which is found to be the best at modelling the nature of the electricity prices. A time series of half-hourly electricity price data from the Hayward node in New Zealand is transformed into a daily average price series and using this resulting series, appropriate models are fitted for estimating and forecasting.  The new EVT-SARIMA model is used to simulate 1000 time series of daily electricity prices, over a 90 day period, to consider strategies for managing the risk associated with price volatility. The effects of different financial instruments on the cumulative distribution functions of predicted revenue obtained using our model are considered. Results suggest that different contracts have different effects on the predicted revenue. However, all contracts have the effect of reducing variability in the predicted revenue values and thus, should be used by a risk manager to reduce the range of probable revenue values. The quantity traded and which contracts to use is dependent on the objectives of the risk manager.</p>

scholarly journals Statistical Analysis of New Zealand Electricity Prices: A Risk Manager's Perspective

2021 ◽  
Author(s):  
◽  
Caroline Moy
Keyword(s):  
Time Series ◽  
New Zealand ◽  
Price Volatility ◽  
Distribution Functions ◽  
Electricity Price ◽  
Cumulative Distribution ◽  
Electricity Prices ◽  
Sarima Model ◽  
Price Data ◽  
Risk Manager

<p>This thesis considers the conventional SARIMA model and the EVT-GARCH model for forecasting electricity prices. However, we find that these models do not adequately capture the important characteristics of the electricity price data. A new model is developed, the EVT-SARIMA model, for forecasting electricity prices which is found to be the best at modelling the nature of the electricity prices. A time series of half-hourly electricity price data from the Hayward node in New Zealand is transformed into a daily average price series and using this resulting series, appropriate models are fitted for estimating and forecasting.  The new EVT-SARIMA model is used to simulate 1000 time series of daily electricity prices, over a 90 day period, to consider strategies for managing the risk associated with price volatility. The effects of different financial instruments on the cumulative distribution functions of predicted revenue obtained using our model are considered. Results suggest that different contracts have different effects on the predicted revenue. However, all contracts have the effect of reducing variability in the predicted revenue values and thus, should be used by a risk manager to reduce the range of probable revenue values. The quantity traded and which contracts to use is dependent on the objectives of the risk manager.</p>

scholarly journals Technical Note: On the intercalibration of HIRS channel 12 brightness temperatures following the transition from HIRS 2 to HIRS 3/4 for ice saturation studies

2016 ◽  
Author(s):  
Klaus Gierens ◽  
Kostas Eleftheratos
Keyword(s):  
Time Series ◽  
Technical Note ◽  
Temperature Data ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Central Wavelength ◽  
Upper Troposphere ◽  
Cumulative Distribution Functions ◽  
Brightness Temperatures

Abstract. In the present study we explore the capability of the intercalibrated HIRS brightness temperature data at channel 12 (the HIRS water vapour channel; T12) to reproduce ice supersaturation in the upper troposphere during the period 1979–2014. Focus is given on the transition from the HIRS 2 to the HIRS 3 instrument in the year 1999, which involved a shift of the central wavelength in channel 12 from 6.7 µm to 6.5 µm. It is shown that this shift produced a discontinuity in the time series of low T12 values ( 70 %) in the year 1999 which prevented us from maintaining a continuous, long term time series of ice saturation throughout the whole record (1979–2014). We present that additional corrections are required to the low T12 values in order to bring HIRS 3 levels down to HIRS 2 levels. The new corrections are based on the cumulative distribution functions of T12 from NOAA 14 and 15 satellites (that is, when the transition from HIRS 2 to HIRS 3 occurred). By applying these corrections to the low T12 values we show that the discontinuity in the time series caused by the transition of HIRS 2 to HIRS 3 is not apparent anymore when it comes to calculate extreme UTHi cases. We come up with a new time series for values found at the low tail of the T12 distribution, which can be further exploited for analyses of ice saturation and supersaturation cases. The validity of the new method with respect to typical intercalibration methods such as regression-based methods is presented and discussed.

scholarly journals Technical note: On the intercalibration of HIRS channel 12 brightness temperatures following the transition from HIRS 2 to HIRS 3/4 for ice saturation studies

2017 ◽  
Vol 10 (2) ◽  
pp. 681-693 ◽  
Author(s):  
Klaus Gierens ◽  
Kostas Eleftheratos
Keyword(s):  
Time Series ◽  
Technical Note ◽  
Temperature Data ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Central Wavelength ◽  
Upper Troposphere ◽  
Brightness Temperatures ◽  
Upper Tropospheric Humidity

Abstract. In the present study we explore the capability of the intercalibrated HIRS brightness temperature data at channel 12 (the HIRS water vapour channel; T12) to reproduce ice supersaturation in the upper troposphere during the period 1979–2014. Focus is given on the transition from the HIRS 2 to the HIRS 3 instrument in the year 1999, which involved a shift of the central wavelength in channel 12 from 6.7 to 6.5 µm. It is shown that this shift produced a discontinuity in the time series of low T12 values ( < 235 K) and associated cases of high upper-tropospheric humidity with respect to ice (UTHi  > 70 %) in the year 1999 which prevented us from maintaining a continuous, long-term time series of ice saturation throughout the whole record (1979–2014). We show that additional corrections are required to the low T12 values in order to bring HIRS 3 levels down to HIRS 2 levels. The new corrections are based on the cumulative distribution functions of T12 from NOAA 14 and 15 satellites (that is, when the transition from HIRS 2 to HIRS 3 occurred). By applying these corrections to the low T12 values we show that the discontinuity in the time series caused by the transition of HIRS 2 to HIRS 3 is not apparent anymore when it comes to calculating extreme UTHi cases. We come up with a new time series for values found at the low tail of the T12 distribution, which can be further exploited for analyses of ice saturation and supersaturation cases. The validity of the new method with respect to typical intercalibration methods such as regression-based methods is presented and discussed.

scholarly journals Forecasting the Intra-Day Spread Densities of Electricity Prices

Energies ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 687 ◽  
Author(s):  
Ekaterina Abramova ◽  
Derek Bunn
Keyword(s):  
Loss Function ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Density Functions ◽  
Shape Parameters ◽  
Electricity Prices ◽  
Dynamic Density ◽  
Cumulative Distribution Functions ◽  
Pinball Loss ◽  
Best Fitting

Intra-day price spreads are of interest to electricity traders, storage and electric vehicle operators. This paper formulates dynamic density functions, based upon skewed-t and similar representations, to model and forecast the German electricity price spreads between different hours of the day, as revealed in the day-ahead auctions. The four specifications of the density functions are dynamic and conditional upon exogenous drivers, thereby permitting the location, scale and shape parameters of the densities to respond hourly to such factors as weather and demand forecasts. The best fitting and forecasting specifications for each spread are selected based on the Pinball Loss function, following the closed-form analytical solutions of the cumulative distribution functions.

scholarly journals Modelling the Cumulative Number of COVID-19 Cases

2021 ◽  
Vol 02 (02) ◽  
pp. 1-1
Author(s):  
Mieczysław Szyszkowicz ◽  
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Series Data ◽  
Cumulative Number ◽  
Daily Time Series ◽  
Non Linear ◽  
The Usa ◽  
Daily Time

Each country has its own characteristics of COVID-19 infection trajectory and epidemic waves. Differences in government-implemented restrictions and social regulations result in variability of the virus transmissions and spread dynamics. This in turn results in various shapes of the growth function used to represent and describe the propagation of infection. Statistical methods are applied to fit non-linear functions to represent daily time-series data of the cumulative numbers of COVID-19 cases. The aim of this work is to fit various statistical models to the cumulative number of COVID-19 cases. Also to overview various types of the existed numerical methodologies. The data (since December 31, 2019) are available for almost each country in the world. As the examples, we used daily time-series data of the cumulative number of COVID-19 cases in Poland, Italy, Canada, and the USA. Non-linear approximations are applied to represent these time series data. The fitted functions allow us to investigate the dynamics of the pandemic. The constructed approximations are compositions of a few nonlinear functions, which describe the growth process of the COVID-19 infection trajectories. Two Gompertz functions and cumulative distribution functions (cdf) were estimated for the data of Poland and Italy (using the cdf for the normal distribution) and for the data of Canada and the USA (using the cdf for the gamma distribution). An analytical (parametric) functions representation of the number of COVID-19 cumulative cases is a useful tool to study the propagation of epidemics.

scholarly journals Drought Hazard Mapping from Regional Climate Multimodel Ensemble over Spain

2015 ◽  
Vol 10 (2) ◽  
pp. 17
Author(s):  
Sandra G. Garcia Galiano ◽  
Juan Diego Giraldo Osorio ◽  
Patricia Olmos Gimenez
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Regional Climate ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Hazard Mapping ◽  
Annual Maximum ◽  
Dry Spells ◽  
Basin Scale ◽  
Spatio Temporal

<p>Improving the knowledge about the impacts of climate change on extreme drought events at basin scale, is important for decision makers in order to develop drought contingency plans which are the leading edge of adaptive management strategy. Considering high-resolution grids of observed daily rainfall and information provided by latest-generation Regional Climate Models (RCMs), the changes in the spatio-temporal patterns of extreme droughts in peninsular Spain are assessed. The non-stationarity character of time series, due to climate and anthropogenic changes, is represented by probabilistic models considering the time evolution of probability density function (PDF) parameters fitted to annual maximum lengths of dry spells time series. By a PDF ensemble from 17 RCMs, the spatio-temporal variability exhibited by the RCMs is represented. Scoring of models is based in the goodness-of-fit to CDFs (cumulative distribution functions) of observed annual maximum dry spells lengths. The reliability and skills of RCMs are assessed, for building the PDF ensemble, at grid site for the study area. Therefore, by adjusting PDF to series of annual maximum dry spells lengths, applying GAMLSS and bootstrapping techniques, the assessment of regional changes and trends associated to high returns periods (<em>Tr</em> = 25 and 50 yr.) is assessed. In general, an intensification of drought events for 2050 horizon, in contrast with 1990, is expected. By increasing return periods, the length of the annual maximum dry spells rises, albeit with a smaller number of areas with significant differences. The areas prone to extreme droughts in mainland Spain are identified.</p>

scholarly journals FIELD STUDIES OF RUN-UP ON DISSIPATIVE BEACHES

1984 ◽  
Vol 1 (19) ◽  
pp. 28 ◽  
Author(s):  
Christopher T. Carlson
Keyword(s):  
Time Series ◽  
Incident Wave ◽  
Wind Waves ◽  
Peak Frequency ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Statistical Hypothesis ◽  
Spectral Energy ◽  
Run Up ◽  
Incident Waves

Field measurements of narrow-band incident wind waves and the resulting run-up were made photographically at two different natural sand beaches along San Francisco Bay. The run-up spectra derived from the field-measured time series show some energy at the incident-wave peak frequency, with the predominant run-up spectral energy concentrated in frequency bands below the incident-wave peak frequency. Observations of the swash time series recorded at both beaches indicate that the low-frequency run-up is generated on the beach face by the interaction between the run-up and backwash during the swash cycle. Coherence analyses indicate that the offshore incident waves and run-up on the beach are not linearly correlated but that the run-up is correlated in the alongshore direction. The slopes of the log-log run-up spectra computed over the frequency band of the incident waves are all approximately -3. Statistical hypothesis tests were used to compare the empirical run-up cumulative distribution functions with both normal and Rayleigh distribution functions.

scholarly journals Time-Series Mapping of PM10Concentration Using Multi-Gaussian Space-Time Kriging: A Case Study in the Seoul Metropolitan Area, Korea

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
No-Wook Park
Keyword(s):  
Time Series ◽  
Metropolitan Area ◽  
Space Time ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Elementary Functions ◽  
Seoul Metropolitan Area ◽  
Deterministic Trend ◽  
Gaussian Space

This paper presents space-time kriging within a multi-Gaussian framework for time-series mapping of particulate matter less than 10 μm in aerodynamic diameter (PM10) concentration. To account for the spatiotemporal autocorrelation structures of monitoring data and to model the uncertainties attached to the prediction, conventional multi-Gaussian kriging is extended to the space-time domain. Multi-Gaussian space-time kriging presented in this paper is based on decomposition of the PM10concentrations into deterministic trend and stochastic residual components. The deterministic trend component is modelled and regionalized using the temporal elementary functions. For the residual component which is the main target for space-time kriging, spatiotemporal autocorrelation information is modeled and used for space-time mapping of the residual. The conditional cumulative distribution functions (ccdfs) are constructed by using the trend and residual components and space-time kriging variance. Then, the PM10concentration estimate and conditional variance are empirically obtained from the ccdfs at all locations in the study area. A case study using the monthly PM10concentrations from 2007 to 2011 in the Seoul metropolitan area, Korea, illustrates the applicability of the presented method. The presented method generated time-series PM10concentration mapping results as well as supporting information for interpretations, and led to better prediction performance, compared to conventional spatial kriging.

Residual-Based Tests for the Null of Stationarity with Applications to U.S. Macroeconomic Time Series

1994 ◽  
Vol 10 (3-4) ◽  
pp. 720-746 ◽  
Author(s):  
In Choi
Keyword(s):  
Time Series ◽  
Unit Root ◽  
Distribution Functions ◽  
Asymptotic Distributions ◽  
Cumulative Distribution ◽  
Finite Sample ◽  
Annual Series ◽  
Cumulative Distribution Functions ◽  
Lm Test ◽  
Macroeconomic Time Series

This paper proposes residual-based tests for the null of level- and trend-stationarity, which are analogs of the LM test for an MA unit root. Asymptotic distributions of the tests are nonstandard, but they are expressed in a unified manner by expressing stochastic integrals. In addition, the tests are shown to be consistent. By expressing the distributions expressed as a function of a chi-square variable with one degree of freedom, the exact limiting probability density and cumulative distribution functions are obtained, and the exact limiting cumulative distribution functions are tabulated. Finite sample performance of the proposed tests is studied by simulation. The tests display stable size when the lag truncation number for the long-run variance estimation is chosen appropriately. But the power of the tests is generally not high at selected sample sizes. The test for the null of trend-stationarity is applied to the U.S. macroeconomic time series along with the Phillips-Perron Z(⋯) test. For some monthly and annual series, the two tests provide consistent inferential results. But for most series, the two contradictory nulls of trend-stationarity and a unit root cannot be rejected at the conventional significance levels.

scholarly journals Analysis of Indonesian and Chinese Garlic Volatility Prices

2019 ◽  
pp. 197-207
Author(s):  
Marina Ayuningtyas ◽  
Sri Hartoyo ◽  
Sri Mulatsih
Keyword(s):  
Time Series ◽  
Garch Model ◽  
Price Volatility ◽  
World Market ◽  
Food Price ◽  
Price Stability ◽  
Price Uncertainty ◽  
Price Fluctuations ◽  
Price Data ◽  
The World

The need for garlic consumption in Indonesia tends to increase without being matched by increased production, which causes Indonesia to import garlic by 95 percent of total domestic needs. Garlic imports tend to increase, causing the price of local garlic to be higher than the price of imported garlic, so consumers prefer imported garlic products over local garlic products. This causes farmers to face the risk of uncertainty (unpredictable) on prices, where price fluctuations are difficult to predict. In order to cope with price fluctuations and to maintain food price stability that remains accessible to consumers, it is necessary to conduct research on the analysis of the price volatility of garlic, so that price uncertainty can be overcome. This study aims to analyze price volatility in the garlic market in Indonesia and China using time series price data between January 2012 and September 2019. The method used is the ARCH/GARCH model. The results showed price volatility at producer level, imported garlic retailers, and the world market (China).

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