scholarly journals SARIMA modeling of the monthly average maximum and minimum temperatures in the eastern plateau region of India

MAUSAM ◽  
2021 ◽  
Vol 67 (4) ◽  
pp. 841-848
Author(s):  
ENAKSHI SAHA ◽  
ARNAB HAZRA ◽  
PABITRA BANIK
Keyword(s):  
Time Series ◽  
Autocorrelation Function ◽  
Minimum Temperature ◽  
Information Criteria ◽  
Temperature Series ◽  
Plateau Region ◽  
Akaike Information Criteria ◽  
Monthly Average ◽  
Standardized Residuals ◽  
Average Maximum

The SARIMA time series model is fitted to the monthly average maximum and minimum temperature data sets collected at Giridih, India for the years 1990-2011. From the time-series  plots, we observe that the patterns of both the series are quite different; maximum temperature series contain sharp peaks in almost all the years while it is not true for the minimum temperature series and hence both the series are modeled separately (also for the sake of simplicity). SARIMA models are selected based on observing autocorrelation function (ACF) and partial autocorrelation function (PACF) of the monthly temperature series. The model parameters are obtained by using maximum likelihood method with the help of three tests [i.e., standard error, ACF and PACF of residuals and Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC) and corrected Akaike Information Criteria (AICc)]. Adequacy of the selected models is determined using diagnostic checking with the standardized residuals, ACF of residuals, normal Q-Q plot of the standardized residuals and p-values of the Ljung-Box statistic. The models ARIMA (1; 0; 2) × (0; 1; 1)12  and ARIMA (0; 1; 1) × (1; 1; 1)12  are finally selected for forecasting of monthly average maximum and minimum temperature values respectively for the eastern plateau region of India.  

scholarly journals Evaluation of Climate Change on Streamflow, Sediment, and Nutrient Load at Watershed Scale

Climate ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 165
Author(s):  
Prem B. Parajuli ◽  
Avay Risal
Keyword(s):  
Climate Change ◽  
Water Quality ◽  
Minimum Temperature ◽  
Future Climate ◽  
Maximum Temperature ◽  
Nutrient Load ◽  
Climate Scenarios ◽  
Monthly Average ◽  
Average Maximum ◽  
Monthly Streamflow

This study evaluated changes in climatic variable impacts on hydrology and water quality in Big Sunflower River Watershed (BSRW), Mississippi. Site-specific future time-series precipitation, temperature, and solar radiation data were generated using a stochastic weather generator LARS-WG model. For the generation of climate scenarios, Representative Concentration Pathways (RCPs), 4.5 and 8.5 of Global Circulation Models (GCMs): Hadley Center Global Environmental Model (HadGEM) and EC-EARTH, for three (2021–2040, 2041–2060 and 2061–2080) future climate periods. Analysis of future climate data based on six ground weather stations located within BSRW showed that the minimum temperature ranged from 11.9 °C to 15.9 °C and the maximum temperature ranged from 23.2 °C to 28.3 °C. Similarly, the average daily rainfall ranged from 3.6 mm to 4.3 mm. Analysis of changes in monthly average maximum/minimum temperature showed that January had the maximum increment and July/August had a minimum increment in monthly average temperature. Similarly, maximum increase in monthly average rainfall was observed during May and maximum decrease was observed during September. The average monthly streamflow, sediment, TN, and TP loads under different climate scenarios varied significantly. The change in average TN and TP loads due to climate change were observed to be very high compared to the change in streamflow and sediment load. The monthly average nutrient load under two different RCP scenarios varied greatly from as low as 63% to as high as 184%, compared to the current monthly nutrient load. The change in hydrology and water quality was mainly attributed to changes in surface temperature, precipitation, and stream flow. This study can be useful in the development and implementation of climate change smart management of agricultural watersheds.

scholarly journals Modeling and Forecasting Periodic Time Series data with Fourier Autoregressive Model

2019 ◽  
pp. 1367-1373
Author(s):  
Abass I. Taiwo ◽  
Timothy Olabisi Olatayo ◽  
Adedayo Funmi Adedotun ◽  
Kazeem kehinde Adesanya
Keyword(s):  
Time Series ◽  
Autocorrelation Function ◽  
Autoregressive Model ◽  
Estimation Method ◽  
Information Criteria ◽  
Series Data ◽  
Percentage Error ◽  
Model Forecast ◽  
Modeling And Forecasting ◽  
Periodic Autocorrelation Function

Most frequently used models for modeling and forecasting periodic climatic time series do not have the capability of handling periodic variability that characterizes it. In this paper, the Fourier Autoregressive model with abilities to analyze periodic variability is implemented. From the results, FAR(1), FAR(2) and FAR(2) models were chosen based on Periodic Autocorrelation function (PeACF) and Periodic Partial Autocorrelation function (PePACF). The coefficients of the tentative model were estimated using a Discrete Fourier transform estimation method. FAR(1) models were chosen as the optimal model based on the smallest values of Periodic Akaike (PAIC) and Bayesian Information criteria (PBIC). The residual of the fitted models was diagnosed to be white noise. The in-sample forecast showed a close reflection of the original rainfall series while the out-sample forecast exhibited a continuous periodic forecast from January 2019 to December 2020 with relatively small values of Periodic Root Mean Square Error (PRMSE), Periodic Mean Absolute Error (PMAE) and Periodic Mean Absolute Percentage Error (PMAPE). The comparison of FAR(1) model forecast with AR(3), ARMA(2,1), ARIMA(2,1,1) and SARIMA( 1,1,1)(1,1,1)12 model forecast indicated that FAR(1) outperformed the other models as it exhibited a continuous periodic forecast. The continuous monthly periodic rainfall forecast indicated that there will be rapid climate change in Nigeria in the coming yearly and Nigerian Government needs to put in place plans to curtail its effects.

Noise Modeling

2017 ◽  
Author(s):  
Richard McCleary ◽  
David McDowall ◽  
Bradley J. Bartos
Keyword(s):  
Time Series ◽  
White Noise ◽  
Autocorrelation Function ◽  
Model Building ◽  
Moving Average ◽  
Information Criteria ◽  
Noise Model ◽  
Adequate Model ◽  
Noise Modeling ◽  
Modeling Strategy

Chapter 3 introduces the Box-Jenkins AutoRegressive Integrated Moving Average (ARIMA) noise modeling strategy. The strategy begins with a test of the Normality assumption using a Kolomogov-Smirnov (KS) statistic. Non-Normal time series are transformed with a Box-Cox procedure is applied. A tentative ARIMA noise model is then identified from a sample AutoCorrelation function (ACF). If the sample ACF identifies a nonstationary model, the time series is differenced. Integer orders p and q of the underlying autoregressive and moving average structures are then identified from the ACF and partial autocorrelation function (PACF). Parameters of the tentative ARIMA noise model are estimated with maximum likelihood methods. If the estimates lie within the stationary-invertible bounds and are statistically significant, the residuals of the tentative model are diagnosed to determine whether the model’s residuals are not different than white noise. If the tentative model’s residuals satisfy this assumption, the statistically adequate model is accepted. Otherwise, the identification-estimation-diagnosis ARIMA noise model-building strategy continues iteratively until it yields a statistically adequate model. The Box-Jenkins ARIMA noise modeling strategy is illustrated with detailed analyses of twelve time series. The example analyses include non-Normal time series, stationary white noise, autoregressive and moving average time series, nonstationary time series, and seasonal time series. The time series models built in Chapter 3 are re-introduced in later chapters. Chapter 3 concludes with a discussion and demonstration of auxiliary modeling procedures that are not part of the Box-Jenkins strategy. These auxiliary procedures include the use of information criteria to compare models, unit root tests of stationarity, and co-integration.

scholarly journals A positive association between cryptosporidiosis notifications and ambient temperature, Victoria, Australia, 2001–2009

2015 ◽  
Vol 13 (4) ◽  
pp. 1039-1047 ◽  
Author(s):  
Lillian Kent ◽  
Michelle McPherson ◽  
Nasra Higgins
Keyword(s):  
Climate Change ◽  
Ambient Temperature ◽  
Rural Areas ◽  
Minimum Temperature ◽  
Negative Binomial ◽  
Negative Binomial Regression Model ◽  
Public Health Response ◽  
Monthly Average ◽  
Average Maximum ◽  
Average Minimum Temperature

Increased temperatures provide optimal conditions for pathogen survival, virulence and replication as well as increased opportunities for human–pathogen interaction. This paper examined the relationship between notifications of cryptosporidiosis and temperature in metropolitan and rural areas of Victoria, Australia between 2001 and 2009. A negative binomial regression model was used to analyse monthly average maximum and minimum temperatures, rainfall and the monthly count of cryptosporidiosis notifications. In the metropolitan area, a 1 °C increase in monthly average minimum temperature of the current month was associated with a 22% increase in cryptosporidiosis notifications (incident rate ratio (IRR) 1.22; 95% confidence interval (CI) 1.13–1.31). In the rural area, a 1 °C increase in monthly average minimum temperature, lagged by 3 months, was associated with a 9% decrease in cryptosporidiosis notifications (IRR 0.91; 95% CI 0.86–0.97). Rainfall was not associated with notifications in either area. These relationships should be considered when planning public health response to ecological risks as well as when developing policies involving climate change. Rising ambient temperature may be an early warning signal for intensifying prevention efforts, including appropriate education for pool users about cryptosporidiosis infection and management, which might become more important as temperatures are projected to increase as a result of climate change.

Comparative analysis of hatchability dynamics (CAHD) of eggs in selected hatcheries in Ibadan metropolis

2020 ◽  
Vol 45 (3) ◽  
Author(s):  
T. O. Dauda ◽  
S. O. Omotoso ◽  
V. A. Ojuade ◽  
V. A. Ojuade ◽  
M. K. Akinwale
Keyword(s):  
Time Series ◽  
Comparative Analysis ◽  
Time Series Analysis ◽  
Information Criteria ◽  
Cyclic Variation ◽  
Summary Statistics ◽  
Akaike Information Criteria ◽  
Egg Hatchability ◽  
Series Analysis ◽  
Time Plot

We carried out this study to evaluate the plausibility of the representativeness of time series analysis results using egg hatchability data from 2 selected hatcheries: Bronco and Foresight hatcheries, Oluyole, Ibadan (both at Latitude 7º 23´ N and Longitude 3º 82´ E). The initial summary statistics of egg variables showed that in Bronco hatchery, the quantity of eggs set peaked (14935.53) in the months of November but lowest (11298.91) in the months of March. However, variance of eggs set in the months of September was highest (41018287) but lowest (1613430) in the months of March. The quantity of fertile eggs ranged between 10216.96 (March) and 13527.58 (November). Total number of chicks produced was highest (11966.15) in the months of November and lowest (9265.86) in the months of March. The time plot of egg set for hatching returned an unconditional cyclic variance and similarly with egg transferred. Although, total eggs hatched into chicks had different time plot pattern but it was also an unconditional cyclic variation. The Jarque-Bera (JB) statistics returned for egg set, egg transferred, total chicks hatched and ratio for Bronco hatchery are 1654.92, 1011.46, 38.721 and 57.855, respectively, while that of foresight hatchery are 25.038, 27.006, 235.897 and 365.734, respectively. The acf(x …x ) of the egg variable presented a wider value than that of acf of (x …x ) for foresight hatchery hence, the acf (x …x ) =(x …x ) could not be said to be strictly stationary. However, the acf of the x …x presented a cyclical and reducing acf like the original acf hence, (x …x ) =(x …x ). The acf of the ratio of egg set to total chicks hatched gave cyclical but reducing trend for both Bronco and Foresight hatcheries. These trends were also maintained for the x …x hence xtk+h …x = x …x . TheARIMAmodel of the ratio of the egg hatchability variables has the least corrected akaike information criteria nd Bayesian Information Criteria hence it could be adjudged the most parsimonious.

scholarly journals Modelling long memory in maximum and minimum temperature series in India

MAUSAM ◽  
2021 ◽  
Vol 68 (2) ◽  
pp. 317-326
Author(s):  
RANJIT KUMAR PAUL
Keyword(s):  
Time Series ◽  
Long Memory ◽  
Minimum Temperature ◽  
Fractional Integration ◽  
Predictive Ability ◽  
Temperature Series ◽  
Weather Data ◽  
Maximum Temperature ◽  
Percentage Error ◽  
Temperature Pattern

Time series analysis of weather data can be a very valuable tool to investigate its variability pattern and, maybe, even to predict short- and long-term changes in the time series. In this study, the long memory behaviour of monthly minimum and maximum temperature of India for the period 1901 to 2007 by means of fractional integration techniques has been investigated. The results show that the time series can be specified in terms of autoregressive fractionally integrated moving average (ARFIMA) process. Both the series were found to be integrated with orders of integration smaller than 0.5 ensuring the long memory stationarity. Wavelet methodology in frequency domain with Haar wavelet filter was applied in order to see the oscillation at different scale and at different time epochs of the series. Multiresolution analysis (MRA) was carried out to explore the local as well as global variations in both the temperature series over the years. The variability in minimum temperature is found to be more than maximum temperature. Though there is no clear significance trend in the temperature series in the long run, but there are pockets of change in the temperature pattern. The predictive ability of ARFIMA model was investigated in terms of relative mean absolute percentage error.

Intervention Modeling

2017 ◽  
Author(s):  
Richard McCleary ◽  
David McDowall ◽  
Bradley J. Bartos
Keyword(s):  
Time Series ◽  
Autocorrelation Function ◽  
Moving Average ◽  
Intervention Model ◽  
Noise Component ◽  
Autoregressive Integrated Moving Average ◽  
Noise Function ◽  
Modeling Strategy ◽  
The Impact ◽  
True Structure

The general AutoRegressive Integrated Moving Average (ARIMA) model can be written as the sum of noise and exogenous components. If an exogenous impact is trivially small, the noise component can be identified with the conventional modeling strategy. If the impact is nontrivial or unknown, the sample AutoCorrelation Function (ACF) will be distorted in unknown ways. Although this problem can be solved most simply when the outcome of interest time series is long and well-behaved, these time series are unfortunately uncommon. The preferred alternative requires that the structure of the intervention is known, allowing the noise function to be identified from the residualized time series. Although few substantive theories specify the “true” structure of the intervention, most specify the dichotomous onset and duration of an impact. Chapter 5 describes this strategy for building an ARIMA intervention model and demonstrates its application to example interventions with abrupt and permanent, gradually accruing, gradually decaying, and complex impacts.

scholarly journals SARIMA Approach to Generating Synthetic Monthly Rainfall in the Sinú River Watershed in Colombia

Atmosphere ◽  
2020 ◽  
Vol 11 (6) ◽  
pp. 602
Author(s):  
Luisa Martínez-Acosta ◽  
Juan Pablo Medrano-Barboza ◽  
Álvaro López-Ramos ◽  
John Freddy Remolina López ◽  
Álvaro Alberto López-Lambraño
Keyword(s):  
Time Series ◽  
Water Resources ◽  
Autocorrelation Function ◽  
Information Criterion ◽  
Monthly Rainfall ◽  
Statistical Characteristics ◽  
Rainfall Time Series ◽  
River Watershed ◽  
Statistical Measures ◽  
Sarima Models

Seasonal Auto Regressive Integrative Moving Average models (SARIMA) were developed for monthly rainfall time series. Normality of the rainfall time series was achieved by using the Box Cox transformation. The best SARIMA models were selected based on their autocorrelation function (ACF), partial autocorrelation function (PACF), and the minimum values of the Akaike Information Criterion (AIC). The result of the Ljung–Box statistical test shows the randomness and homogeneity of each model residuals. The performance and validation of the SARIMA models were evaluated based on various statistical measures, among these, the Student’s t-test. It is possible to obtain synthetic records that preserve the statistical characteristics of the historical record through the SARIMA models. Finally, the results obtained can be applied to various hydrological and water resources management studies. This will certainly assist policy and decision-makers to establish strategies, priorities, and the proper use of water resources in the Sinú river watershed.

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