After checking the goodness-of-fit and forecasting ability of the **model** you can now use the **model** to forecast over a future time horizon. Using the data obtained from January-1990 to December 2013, best fitted **SARIMA** **model** was used to forecast monthly Imports and Exports for Jan.- 2014 to Dec.- 2020.Forecasting Performance of the chosen **SARIMA** **model** is measured using Paired T-test. Paired T- test compares the means between two related samples on the same continuous dependent variable in order to determine whether they vary from each other in a significant way under the assumptions that the paired differences are independent and identically normally distributed. [22]

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The identification step is to tentatively choose one or more **SARIMA** **model**(s) using the estimated ACF and PACF plots. The ACF plot of the AR (Auto-Regressive)/ SAR (Seasonal Auto-Regressive) process shows an exponential decay while its PACF plot truncates at lag $ /seasonal lag P and diminishes to zero afterward. The ACF plot of the MA process truncates to zero after lag % / seasonal lag Q while its PACF decays exponentially to zero. The two processes: AR (p)/SAR (P) and MA (q)/SMA (Q), could be combined to form the ARMA (p, q)/SARMA (P, Q) process which has ACF and PACF that decays exponentially to zero. The non- linear least square estimation method could be used to estimate the parameters of the identified **model**(s) in the identification stage. The last diagnostic checking stage involves assessing the adequacy of the identified and fitted models through a possible statistically significant test on the residuals to verify its consistency with the white noise process e.g. the Ljung-Box test [11]. The ACF and PACF plots of the **SARIMA** **model** (p, 1, q)(P, 1, Q) 12 with first

scholars use mathematical or statistical models to study the time pattern, such as analysing the time series data of theft crimes based on the X11 seasonal adjustment method[1]. There are many methods commonly used in seasonal time series analysis, including seasonal decomposition method, concentration degree method, circular distribution method, ARIMA **model**, **SARIMA** **model**[2], X12 seasonal adjustment method, X11-ARIMA **model**[3], X12-ARIMA **model**[4], X13-ARIMA **model**, as well as TRAMO SEATS **model**. paper makes analysis by both **SARIMA** **model** and X13-ARIMA-SEATS the effect of the mobile holidays (the Spring Festival, Tomb-sweeping Day, Dragon Boat Festival and Mid-Autumn Festival) has to be considered. PBC (department of investigation and statistics of the people's bank of China)

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( )(1 − ) = ( ) (1) The ARIMA methodology is carried out in three stages, viz. identification, estimation and diagnostic checking. Parameters of the tentatively selected ARIMA **model** at the identification stage are estimated at the estimation stage and adequacy of selected **model** is tested at the diagnostic checking stage. If the **model** is found to be inadequate, the three stages are repeated until satisfactory ARIMA **model** is selected for the time-series under consideration. An excellent discussion of various aspects of this approach is given in Box and Jenkins [3]. Most of the standard software packages, like SAS, and RGui contain packages and procedures for fitting of ARIMA models.

Many researchers have used time series analysis to forecast the different variables. Review of some past studies have been done in this section. Abeysinghe (1994) showed that using seasonal dummies in removing seasonality will likely produce spurious regression. Therefore, it was important to identify the nature of seasonality exhibited in the series prior to making any treatment to the seasonality and before deciding on a correct forecast **model** that can control for the seasonality. Qu and Zhang (1996) applied an autoregressive **model** to forecast tourist arrivals in 12 tourist destinations. Kanungo, D. P., et al. (2006) discussed that ANN modeling approach had numerous advantages over conventional phenomological, as ANN structure just require data set and don’t need to follow any assumption about the underlined data set. Rabenja et al. (2009) utilized seasonal ARIMA and non-seasonal ARIMA for forecasting of monthly rainfall as well as discharge of the Namorona River in the Vohiparara River Basin of Madagascar. Study revealed that seasonal ARIMA was more efficient for forecasting these variables as compare to non- seasonal ARIMA. Gijo (2011) used time series data of demand of tea for India. The underline series was modeled by Box-Jenkins seasonal auto regressive integrated moving average (**SARIMA**) **model**. Adequacy of the fitted **model** was tested by using Lung-Box test criteria followed by residual analysis. Hamidreza and Leila (2012) utilized SARFIMA **model** to study and predict the Iran’s oil supply. The results showed that the best **model** was SARFIMA (0,1,1)(0,-0.199,0) 12 which was used to predict the quantity of oil supply in

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As the intermediate target of monetary policy, money supply is one of the im- portant means of macroeconomic regulation. It includes narrow money supply and broad money supply. The difference between the two is that the former does not include guasi-money. For a country or a region, money supply will affect its inflation rate. Generally, the central bank will take the total money supply as the main means of regulation to keep the currency stable. In addition, money supply is also crucial to the development of capital market. Changes in money supply will lead to the changes of market interest rates, which have an effect on the in- vestment costs and profits of listed companies and ultimately make the company stock change. Chen Riqing and Wang Tongtong (2011) [1] analyzed the nonli- near effects of the money supply on Chinese insurance market by building the Markov regime switching **model**. Gu Liubao and Chen Bofei (2013) [2], by building the VAR **model**, used impulse response function and variance decom- position to analyze the dynamic affection of the changes of money supply and interest rate on the price of real estate market. Zhang Xiuli (2011) [3] analyzed the correlation between money supply and stock price. In fact, scholars had less How to cite this paper: Shen, S.C. and

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Because the **SARIMA** **model** had been used to analyze the linear part of the actual data, the residuals should con- tain nonlinear relationships. In **SARIMA**- GRNN **model**, we combined the linear and nonlinear parts of the models. We selected the monthly estimated incidence number of TB at time variable t from the **SARIMA** **model** and time variable t as two input variables. There is one output vari- able y which was the actual reported monthly incidence number of TB. The iterations of GRNN learning and simulating data was conducted in Matlab 7.0 software package (Math Works Inc., Natick, MA, USA) to deter- mine the relationship between the input and output variables.

Actually, it should be impossible to laboratory test for all death. Alternatively, estimation of influenza associated death from their last symptoms leads to dras- tic underestimation. Instead of counting influenza associated death, “excess mortality” was estimated using a statistical **model** with consideration of the pat- tern of fluctuation of non influenza associated death. In fact, WHO used Serfling **model** [7]. Furthermore, it had been adopted by the Center for Disease Control and Prevention (CDC) in the USA after modification. However, because the Ser- fling **model** excludes past epidemic seasons, the possibility exists that the num- ber of excess mortality might be underestimated when the influenza epidemic was relatively small [8]. Moreover, the current CDC **model** uses only the latest five years; it might not use sufficient information. On the other hand, Choi and Thacker [8] adopted the seasonal autoregressive integrated moving average (**SARIMA**) **model** to estimate influenza and pneumonia death using data in the “non-epidemic seasons” when no influenza outbreak occurred, especially in summer. They defined “non-epidemic seasons” from widespread reporting to CDC from the states and information of influenza virus isolation. However, it sounds artificial. Moreover, they defined the number of deaths caused by in- fluenza in epidemic season if influenza did not outbreak as the reverse pattern in “non-epidemic” seasons. Such a definition is apparently too rough and probably leads to underestimate excess mortality. The Serfling **model** also shared those shortcomings in **SARIMA** **model**. In Japan, some studies proposed to estimate excess mortality had been as a simple average so far [9] [10] [11]. Therefore, they were not precise estimations.

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Using the obtained **SARIMA** **model** to predict the throughput of container ports nationwide and get the forecast conclusion. As shown in Table 2, it can be seen from the results that throughput will continue to increase in the future, de- creasing in February of each year and increasing in December.

Malaysia is one of the top countries that produces natural rubber and was ranked sixth place globally. The earnings from natural rubber products are making billions of ringgit for the country. However, over the past years the natural rubber production in Malaysia has been inconsistent and the deficiencies in the production can affect Malaysia’s economy. Therefore, it is important for relevant agencies and departments to understand the patterns and trends of natural rubber production in Malaysia besides having the ability to forecast. Hence, the integrated autoregressive moving average (ARIMA), seasonal autoregressive moving average (**SARIMA**) and the seasonal Holt-Winter’s **model** were being considered for the purpose of modelling and forecasting this study. The forecast accuracy criteria used to evaluate the performance of the models are the root mean square error (RMSE) and mean absolute percentage error (MAPE). The results showed that the seasonal Holt-Winter’s **model** appeared to be the best **model** as it yielded the lowest RMSE and MAPE values. The seasonal Holt- Winter’s **model**, however, is not a good choice of **model** as it was unable to forecast six months ahead values. On the other hand, the **SARIMA** **model** had a better forecast ability when forecasting the values for the same duration. Therefore, the **SARIMA** **model** is taken to be the **model** in forecasting the natural rubber production in Malaysia for that period. This study has shown that the best fit **model** that fulfil all the forecast accuracy criteria may not have the best forecast ability.

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In this study, the augmented Dickey-Fuller Unit Root (ADF) test was applied to estimate the stationarity of the time series. 26,27 If the time series is not stationary, an appropriate difference can be used to make the series stationary. The Box and Jenkins method was used to con- struct the **SARIMA** **model** in this study. 28 The autocorrela- tion functions (ACF) and partial autocorrelation functions (PACF) of the transformed data were utilized to determine the seasonal and non-seasonal orders and identify an appropriate **SARIMA** **model**. The conditional least squares method was applied to estimate the **model** parameters. In **model** diagnosis, white-noise test methods were employed to check whether the residuals were independent and nor- mally distributed. 29 Several models can be constructed, and the selection of an optimal **SARIMA** **model** is neces- sary. The **model** selection was conducted based on normal- ized Bayesian information criterion (BIC) and Ljung-Box Q test. In addition, coef ﬁ cient of determination (R 2 ), root-

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Czerwinski et al., 2007). The value of the AIC of the selected **SARIMA** **model** was -661.93 as shown in the Table 1. The **SARIMA** (1, 1, 0) (2, 1, 1) 12 , was therefore selected as the most suitable **model** for forecasting Lake Malawi water levels given that it had the lowest AIC values. The most competing models identified together with their corresponding fit statistics are shown in Table 1. The Box–Pierce (and Ljung–Box) test also showed that **model** (1, 1, 0) (2, 1, 1) 12 was among the best fitting models as it had its p-value close to one (1) as shown in Figures 4. The Box–Pierce test basically examines the null of independently distributed residual errors, derived from the idea that the residual errors of a “correctly specified” **model** are independently distributed. In a case where the residual errors are not independently distributed, then it indicates that they come

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Regarding the objective of the study to fore- cast the API with highest accuracy, various ac- curacy measurements have been tested. This includes the measurements based on the mag- nitude of forecasted and observed and the model’s validation based on the ability to fore- cast the exceedances of the assigned limit value. Comparing the three models using magnitude error measurements (MAPE, MAE, MSE, RMSE), the hybrid **model** showed better skills in forecasting API compared to **SARIMA** **model** and ANNs **model**. If comparing the three models based on model’s validation us- ing exceedances indices, the hybrid **model** gives the best result in forecasting the capability to forecast these exceedances with a limit value of 50. Therefore, we can conclude that the hybrid method can be used for future forecasting of air pollutants since it is able to outperform single methods. For example, predicting the real data usually contains both linear and nonlinear pat- tern. In addition, in research on air quality con- cerning the guidelines in order to control the pollution, the chosen best forecast must con- sider the indices based on exceedance threshold value together with the statistical performance using the magnitude error.

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In order to construct the **SARIMA** **model**, we first need to create 11 dummy variables (named D1 to D11, respectively) to represent 12 months of the year. Next, we will regress inflation by a constant and 11 dummy variables, then save the residual number in Table 4. This residual part will be further processed by the ARIMA **model** procedures. Then, the ARIMA **model** will be used to forecast the surplus. Finally, the residual part is included in the initial regression equation for predicting inflation. The data processing results show that the ARIMA **model** (1,0,5) corresponds to the existing residual part shown in Table 5. Combined with the seasonality of inflation, this **model** has named **SARIMA** (1,0,5). The detailed forecast of the **SARIMA** **model** (1,0,5) is shown in Table 3.

A descriptive analysis was conducted to assess the distri- bution of mumps cases and weather factors in Beijing. Seasonal autoregressive integrated moving average (SAR- IMA) models were then used to evaluate relationships between monthly numbers of mumps cases and me- teorological parameters. **SARIMA** models were optimal for use in this study because seasonal and non-seasonal trends could be studied [21]. A **SARIMA** **model** is de- scribed as an autoregressive integrated moving average, p, d, and q, multiplied by P, D, and Q—where the non-seasonal parameters are the number of autoregres- sive terms (p), the number of differences (d), and the moving average (q), and the seasonal parameters are the number of seasonal autoregressive terms (P), the num- ber of seasonal differences (D), and the seasonal moving average (Q).

Outbreaks since diagnostic checks revealed its adequate for predicting the monthly number of fire outbreaks in Ashanti Region of Ghana. The sixteen years forecast with this **model** revealed that the number of fire outbreaks will continue to increase with time. This continuous increase in the pattern of the number of fire outbreaks as evident from the forecast results could be a great danger to the economy of the country. The results achieved for fire forecasting will help to estimate number of fire events which can be used in planning the fire activities in that region. The study recommends that, stakeholders and management of fire should make use of this formulated **SARIMA** **model** for the purpose predicting, mitigating and insuring against fire outbreaks in Ghana.

In conclusion, this paper contributes to exploration of prediction method to forecast outpatient visits in China’s large hospitals. We compared the forecast accuracy of a **SARIMA** **model**, a SES **model**, and that of a combinator- ial **model** by combining **SARIMA** **model** with SES **model** for short-term daily outpatient visits forecasting. All of the selection models are relatively simple in terms of im- plementation and of low computational intensiveness, whilst being appropriate for short-term prediction. And compared simple models, the combinatorial **model** can more effectively extract depth information from a finite training sample size, and achieve better performance for predicting daily outpatient visits 1 week ahead, with lower residuals variance and relative small mean of re- sidual errors which needs to be optimized deeply on the next research step. Also, the results can be used to sup- port the decisions of outpatient resource planning and scheduling. It helps hospital managers to implement periodical scheduling of available resources on the basis of periodic features, as well as the proactive scheduling of additional resources based on the increasing regularity caused by the day of the week effect.

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flexible and captures many different types of patterns [9]. The key concept in the **SARIMA** **model** is the order, which is the differencing. AR is an Autoregressive **Model**; it is one of the categories of **SARIMA** and has been classified as AR(q). The AR includes predictors that are lagged versions of the series. A more complex **model** is the Autoregressive Moving Average **Model**, and has been classified as ARMA: (p, q). The ARMA **model** includes predictors, in addition to the p-lagged series and q-lagged versions of the forecast errors. This forecast error is called the moving average component of this **model**. The concept of ARMA **model** is to capture all forms of autocorrelation by including lags of the series and the forecast errors [9]. **SARIMA** (p, d, q) is the latest upgraded **model** of the previous algorithms of AR and ARMA. The differencing method is compatible and can be applied in the **SARIMA** **model**, which has two sets of parameters, which are (p, d, q) and (P, D, Q). The lowercase d refers to the lag-1 differencing and the uppercase D refers to the seasonal differencing. For a cycle with M seasons, the lag-M differencing is used to remove the seasonality. The parameter values of uppercase D denote decisions whether to perform seasonal differencing: 0 indicates that no seasonal differencing will be executed; and 1 indicates that seasonal differencing will be executed once. The **SARIMA** **model** requires the user to specify the parameter values of (p, d, q) and (P, D, Q) [9]. The **SARIMA** **model** contains many flexible techniques that capture the autocorrelations in all kinds of forms. It has a strong statistical foundation, and it is easy to obtain automated prediction intervals. **SARIMA** does require a stationary series which has no trend, no seasonality, and constant autocorrelation. The **SARIMA** method contains a strong underlying mathematical and statistical theory, and it is easy to generate the predictive intervals. The equations from (1) to (7) are based on the study

In this research, I have explored a methodology for the development of efficient electronic real time data processing system to recognize the behaviour of an elderly person. The ability to determine the wellness of an elderly person living alone in their own home using a robust, flexible and data driven artificially intelligent system has been investigated. A framework integrating temporal and spatial contextual information for determining the wellness of an elderly person has been modelled. A novel behaviour detection process based on the observed sensor data in performing essential daily activities has been designed and developed. The **model** can update the behaviour knowledge base and simultaneously execute the tasks to explore the intricacies of the generated behaviour pattern. An initial decline or change in regular daily activities can suggest changes to the health and functional abilities of the elderly person.

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Malaria case numbers are influenced by factors intrinsic to malaria such as infectivity, immunity and susceptibility of vectors and humans, and extrinsic, environmental factors such as rainfall. The number of possible models for malaria prediction is infinite. In biological process mod- els, typically consisting of sets of equations, prediction can be done with details of all pathways, parameters and variables believed to be important for the dynamics of the disease [15]. In statistical models, temporal or spatial autoregressive terms account for the fact that case num- bers depend on past or nearby case numbers through (sometimes cyclical) intrinsic processes, as well as for (unobserved) extrinsic auto correlated factors or factors with fading effects. This study was limited to some statis- tical models that are relatively easily implemented (with- out taking into consideration complex biological processes and their parameters), and/or that have been successful elsewhere in malaria forecasting studies. With sufficient temporal autocorrelation in malaria case time series, malaria cases can be predicted based on previous values [16]. However, predictions from statistical models are made under the assumption that the relationships established based on past observations remain the same in the future. Therefore, statistical models require experi- ence with as wide a spectrum of conditions as possible. In this light, the present low case numbers, have been unprecedented in the time series under study, and a cau- tion should be in place. More complex statistical models can be constructed where malaria incidence in an area is, apart from its own previous values, also dependent on (previous) values in neighbouring areas, or covariates such as rainfall [17,18]. These latter models require more inputs and therefore more resource intensive to apply, particularly where covariate data need to be acquired and processed in a timely manner to be useful for forecasting. In this paper, it was examined which standard time series statistical **model** would be useful for forecasting malaria, and it was examined whether addition of rainfall to autoregressive models could improve malaria prediction in districts with one to four month forecasting horizons. Methods

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