Univariate Autoregressive Integrated Moving Average Research Articles

The river runoff forecast based on the modeling of time series

Discussed are the methods of stochastic modeling the precipitation runoff time series and fields. Discussed are the structural attributes, scope, boundary conditions and various improvements of the univariate Autoregressive Integrated Moving Average (ARIMA) and the multivariate Transfer Function Model (TFM). Presented are the comparative studies of existing models of the neural network. An attempt is made to investigate various geographical locations and various applications of the river runoff forecast.

Modeling the price of trends of teak wood using statistical and artificial neural network techniques

Modeling the trends and patterns in financial data is of great interest to the business community to support the decision-making process. In this study, the historical trends in the real prices of teak wood were described using spline models and the time periods for which the rate of change in real prices differed were identified. The possible reasons for this phenomenon such as impact of forest legislations and other factors have been explained. In forecasting teak wood prices, Artificial Neural Network (ANN) was compared with the traditional Auto Regressive Integrated Moving Average (ARIMA) model. The Mean Absolute Percentage Error (MAPE) was lesser in the case of ANN than the ARIMA model. Further, the turning points were more closely predicted by ANN. It appeared that forecast by ANN was heavily dependent on the previous value(s) immediate to the forecasting year. The study concluded that the next year price forecasts by univariate ARIMA and ANN models may be far from actual prices due to unanticipated factors.

Wealth based fisheries management of chambo (Oreochromis spp.) fish stock of Lake Malombe in Malawi

A study to establish bioeconomic options for economic exploitation of Chambo (Oreochromis spp.) fisheries of Lake Malombe was conducted between 2010 to 2012. Three models, logistic regression, Univariate Autoregressive Integrated Moving Average and Gordon Schaefer bioeconomic models were used in the analysis. Primary qualitative and quantitative data from fishers and consumers were collected using a pretested semi structured questionnaire. Time series data from 1976 to 2011 was generated from the Traditional Fishery Data Base at Fisheries Research Station. The logistic regression analysis showed that the goodness of fit Hosmer and Lemeshow test yielded c2 (8) of 6.924 and was insignificant at 0.05 (P = 0.214). The -2 Log Likelihood showed that the model fitted the data at an acceptable level (P = 0.001). Six predictor variables (stratum, marital status, literacy, years in fishing and daily working hours) were significant. Autoregressive Integrated Moving Average model (0, 1, 1) was selected. From the selected model, at the current exploitation rate it was forecasted that Chambo catches would decline to -1,111.80 tons in 2021 from 4,118 tons in 1976. From the Gordon Schaefer dynamic model, it is estimated that the economic rent at maximum economic yield, is MK2.148 million as compared to MK1.533 million at maximum sustainable yield. The Gordon Schaefer bioeconomic model showed that high economic rents are associated with maximum economic yield than maximum sustainable yield. Based on the bioeconomic analysis, it is recommended that Chambo fisheries be managed at maximum economic yield, which implies reducing the current fishing effort. Key words: Logistic model, Lake Malombe, forecasting, bioeconomics, economic rent.

ANN hybrid model versus ARIMA and ARIMAX models of runoff coefficient

• We modeled monthly direct runoff coefficients to forecast a holdout dataset. • Initially, we used univariate ARIMA, multivariate ARIMAX, and ANN models. • We found the applied traditional model performances insufficient. • We developed a new Hybrid approach by using time series decomposition and ANN. • We found that the new generated model is superior, suitable for complicated data. In this study, monthly runoff coefficients of seven southern large basins are calculated and modeled to forecast a holdout dataset by using univariate autoregressive integrated moving average (ARIMA), multivariate ARIMA (ARIMAX), and Artificial neural network (ANN) models. The applied traditional model performances are found insufficient, since the characteristic behaviors of the time series of direct runoff coefficients are very complicated. Therefore, a new Hybrid approach is adopted by using time series decomposition procedure and ANN. ARIMA, ARIMAX, ANN, and Hybrid models are compared with each other. The results indicate that the new generated Hybrid approach can be generalized to boost the prediction capability of ANNs in complicated time series data. It is seen that the new model captures the physical behavior of the direct runoff coefficient time series. The semi-random spikes of the direct runoff coefficient series are approximated sufficiently.

Modeling and forecasting pelagic fish production using univariate and multivariate ARIMA models

Univariate and multivariate autoregressive integrated moving average (ARIMA) models were used to model and forecast the monthly pelagic production of fish species in the Mediterranean Sea during 1990–2005. Autocorrelation (AC) and partial autocorrelation (PAC) functions were estimated, which led to the identification and construction of seasonal ARIMA models, suitable in explaining the time series and forecasting the future catch per unit of effort (CPUE) values. Univariate and multivariate ARIMA models satisfactorily predicted the total pelagic fish production and the production of anchovy, sardine, and horse mackerel. The univariate ARIMA models demonstrated a good perpormance in terms of explained variability and predicting power. The current findings revealed a strong autoregressive character providing relatively high R 2 and satisfactory forecasts that were close to the recorded CPUE values. The present results also indicated that the multivariate ARIMA outperformed the univariate ARIMA models in terms of fitting accuracy. The opposite was evidenced when testing the forecasting accuracy of the two methods, where the univariate ARIMA models overall performed better than the multivariate models. The observed seasonal pattern in the monthly production series was attributed to the intrinsic nature of the pelagic fishery. As anchovy, sardine, and horse mackerel represent main target species in the Mediterranean pelagic fishery, the findings of the present study provided direct support for the potential use of accurate forecasts in decision making and fisheries management in the Mediterranean Sea.

Establishment of a Box-Jenkins Multivariate Time-Series Model to Simulate Ground-Level Peak Daily One-Hour Ozone Concentrations at Ta-Liao in Taiwan

Box-Jenkins univariate autoregressive integrated moving average (ARIMA) and regression with time-series error (RTSE) models were established to simulate historical peak daily 1-hr ozone concentrations at Ta-Liao, Taiwan, 1997– 2001. During 1995–2003, the 600 days of Pollution Standard Index (PSI) more than 100 (peak daily 1-hr ozone concentrations detected by greater than 120 ppm) at Tao-Liao showed the highest ozone exceedances among the six monitoring stations in Kaohsiung County. To improve the predictability of extremely high ozone, two different principal components, PC1 and PC(1 + 2), were introduced in the RTSE model. Four typical predictors (particular matter with an aerodynamic diameter less than or equal to 10 μm, temperature, wind speed, and wind direction) plus a PC trigger remained significant in the RTSE model. The model performance statistics concluded that the RTSE model with PC1 was optimal, compared with the univariate ARIMA, the RTSE model without PC, and RTSE model with PC(1 + 2). The contingency table shows that the successful predictions of the univariate model were only 12.9% of that of the RTSE model with PC1. Also, the POD value was improved approximately 5-fold when the univariate model was replaced by the RTSE model, and almost 8-fold when it was replaced by the RTSE model with PC1. Moreover, introducing the PC trigger indeed enhanced the ozone predictability. After the PC trigger was introduced in the RTSE model, the POD was increased 69.9%, and the FAR was reduced 8.3%. The overall correlation between the observed and simulated ozone was improved 9.6%. Also, the first principal component was more useful than the first two components in playing the “trigger” role, though it counted only for<br/>58.62% of the environmental variance during the high ozone days.

Forecasting Foreign Direct Investment Inflow in Jordan: Univariate ARIMA Model

The present study is an attempt to build a Univariate time series model to forecast the FDI inflows into Jordan over the coming period 2004-2025. The study employs Box-Jenkins methodology of building ARIMA (Autoregressive Integrated Moving Average) model to achieve the goals of the study. An annual sample time series data for the FDI in Jordan was utilized over the period 1976-2003. The data were collected from the Central Bank of Jordan publications. The accuracy of the selected models was tested by performing different diagnostic tests to ensure the accuracy of the obtained results. Results of the study show that ARIMA model provides a better model for forecasting FDI in Jordan. The empirical results of ARIMA model have shown that FDI is following an increasing trend over the forecasted period (2004-2025). The empirical results indicate the expected positive impact of FDI inflows on different macroeconomic variables in Jordan economy.

The Predictability of the Amman Stock Exchange using the Univariate Autoregressive Integrated Moving Average (ARIMA) Model

This study examines the univariate ARIMA forecasting model, using the Amman Stock Exchange (ASE) general daily index between 4/1/2004 and 10/8/2004; with out‐of‐sample testing undertaken on the following seven days. Different diagnostic tests were performed to find the best model describing the data. The selected model predicted that the ASE would continue to grow by 0.195% for seven days starting on 11/8/2004. This forecast, however, was not consistent with actual performance during the period of the prediction (11/8/2004 ‐ 19/8/2004) since ASE declined by ‐ 0.003% assuring the fact that ASE followed most closely the Efficient Market Hypothesis (EMH) in its weak form.

Forecasting the Suez Canal traffic: a neural network analysis

Although the Suez Canal is the most important man-made waterway in the world, rivaled perhaps only by the Panama Canal, little research has been done into forecasting its traffic flows. This paper uses both univariate ARIMA (Autoregressive Integrated Moving Average) and Neural network models to forecast the maritime traffic flows in the Suez Canal which are expressed in tons. One of the important strengths of the ARIMA modelling approach is the ability to go beyond the basic univariate model by considering interventions, calendar variations, outliers, or other real aspects of typically observed time series. On the other hand, neural nets have received a great deal of attention over the past few years. They are being used in the areas of prediction and classification, areas where regression models and other related statistical techniques have traditionally been used. The models obtained in this paper provide useful insight into the behaviour of maritime traffic flows since the reopening of the Canal in 1975—following an 8-year closure during the Arab–Israeli wars (1967–1973)—till 1998. The paper also compares the performance of ARIMA models with that of neural networks on an example of a large monthly dataset.

Tourism Forecasting and its Relationship with Leading Economic Indicators

This article investigates the application of three time-series forecasting techniques, namely, exponential smoothing, univariate Autoregressive Integrated Moving Average (ARIMA), and adjusted ARIMA to predict travel demand (i.e., the number of arrivals) from different countries to Hong Kong. The third approach, adjusted ARIMA, is an enhancement of univariate ARIMA. This uses influential economic indicators that are highly correlated with travel demand to adjust univariate ARIMA. According to the analysis, adjusted ARIMA with economic indicators seems to be the best forecasting method for Japan, whereas univariate ARIMA is the best predictor for the United States and United Kingdom. Univariate ARIMA and adjusted ARIMA behave similarly for countries like Taiwan, Singapore, and Korea. Among the three forecasting methods, exponential smoothing is the least accurate. This shows that univariate ARIMA and adjusted ARIMA are more suitable and can be applied to forecast the fluctuating series of visitor arrivals.

Modelling and forecasting annual fisheries catches: comparison of regression, univariate and multivariate time series methods

In the present work, eight forecasting techniques are evaluated on the basis of their efficiency to model and provide accurate operational forecasts of the annual commercial landings of 16 species or groups of species in the Hellenic (Greek) marine waters. The development of operational forecasts was based on the following four general categories of forecasting techniques: (a) deterministic simple or multiple regression models incorporating different exogenous variables (time-varying regression, TV; multiple regression models incorporating time, fishing effort, wholesale value of catch and climatic variables, MREG); (b) univariate time series models (Brown's one parameter exponential smoothing, BES; Holt's two parameter exponential smoothing, HES; and AutoRegressive Integrated Moving Average (ARIMA)); (c) multivariate time series techniques (harmonic regression, HREG; dynamic regression, DREG; and vector autoregressions, VAR); and (d) the ‘biological’ exponential surplus-yield model, FOX. Fits (for 1964–1987) and forecasts (for 1988–1989) obtained by the different models were compared with each other and with those of a naive method (NM) and an empirical one (i.e. combination of forecasts, EMP) using 32 different measures of accuracy. The results revealed that HREG and MREG models outperformed, in terms of fitting accuracy, the remaining eight models (NM, TV, BES, HES, FOX, ARIMA, VAR and EMP). They were both characterised by: (a) higher accuracy in terms of all, or most, standard and relative statistical measures; (b) unbiased fits; (c) much better performance than NM; (d) transformed errors which were essentially white noise. In addition, HREG and MREG models: (e) explained from 79% to 97% of the variability of 13 transformed annual catches and from 31% to 61% for the remaining ones; (f) produced fits with MAPE values ranging from 3.4% to 21.2%; (g) in all, or most cases, predicted the between year variations during the fitting period, 1964–1987. In terms of forecasting performance, however, not a single best approach was found for the 16 annual catches. In general, BES and, to a lesser extent, HES, NM (which actually is an ARIMA (0,1,0)), EMP and HREG models were among the best performers more often, produced the worst forecasts more rarely and were generally characterised by the higher number of stable forecasts and of forecasts with MAPE <20% and <10%. TV was also efficient for some annual series. Conversely, the poorest performers (FOX, MREG and ARIMA) rarely did better than average. The biological FOX models produced the least accurate and biased fits, bad forecasts (> 34.1%) in two out of four cases, and were characterised by transformed errors that were significantly ( P < 0.05) autocorrelated. Some of the empirical models also had interesting explanations. Hence, the univariate ARIMA and multivariate VAR time series models predicted persistence of catches. The multivariate VAR and HREG time series models also predicted cycles in the variability of the catches with periods of 2–3 years. Moreover, FOX and MREG models indicated that fishing effort, wholesale value of catch and climate may, in a synergetic fashion, affect long-term trends and short-term variation in the catches of, at least, some species (or groups of species). Finally, MREG and VAR models predicted that variability and replacement of anchovy by sardine catches are not due to chance, and wind activity over the northern Aegean Sea may act as a forcing function.

Univariate ARIMA forecasts of defined variables: the case of real economic variables

This paper provides additional evidence on whether indirect or direct autoregressive-integrated-moving average (ARIMA) model point forecasts of defined variables are better. Seven monthly real or constant-dollar economic variables for the postwar U.S. over the period 1959–1986 are examined. The variables include three real ex-post interest rates on government securities of varying maturity, two real monetary aggregates, a real wage, and a real foreign exchange rate. Univariate ARIMA models are identified and estimated for the within-sample period from January 1959 to December 1982 using the techniques of Box and Jenkins. Out-of-sample, updated, one-step-ahead tbrecasis are then made for the period January 1983 to December 1986 in order to compare the post-sample accuracy of the indirect and direct forecasts. The criteria of mean absolute error, mean squared error, and mean percentage error are used to evaluate forecast accuracy. In contrast to the findings of Kang, the results show that direct forecasts generally perform heller than indirect forecasts for the set of defined variables examined

TIMCAI: An interactive program to assist in the identification of univariate nonseasonal nonmixed ARIMA time series

The need for accurate statistical techniques in the interpretation of time-series data is crucial for many social-psychological studies. While many techniques have been proposed and debated, the technique initially proposed by Box and Tiao (1965) known as autoregres­ sive integrated moving average (ARIMA) modeling seems to show promise. While much has been written about the technique, there seems to be some reluctance on the part of the social-psychological community to use it when appropriate. One of the major reasons for this reluctance may be due to difficulties in the initial step of identify­ ing an appropriate ARIMA model. Other reasons for the reluctance have been discussed elsewhere (Brown, 1980; McCleary & Hay, 1980). The Box-Tiao approach is an iterative process encom­ passing several stages of development, with the initial step requiring a tentative model identification. This identification step basically relies on two statistics: (1) the autocorrelation function (AUCF) and (2) the partial autocorrelation function (PACF). Autocorrela­ tion refers to the correlations among successive data points separated by each different observation (lag) in the series. Partial autocorrelation refers to the autocorre­ lation of a series with the influence of previous time points partialed out. These two functions are calcu­ lated on the time-series data and generally supplied to the users as a correlogram, or a plot of the autocorrela­ tion and partial autocorrelation as a function of K lags. It is from an ocular analysis of the correlograms that a tentative ARIMA model may be identified. This ocular analytic technique basically compares the estimated AUCF and PACF with theoretical or expected functions, according to a variety of basic ARIMA models. Ambi­ guity in these estimated functions is then lessened by either placing an approximate 95% confidence band around each function (±2 standard errors) or by calcu­ lating a t-like statistic (Bowerman & O'Connell, 1979). The t-like statistic, for both functions, is simply the value of each AUCF and PACF over their respective standard errors at each lag period. The purpose of this software is to assist users in their ocular identification of an appropriate ARIMA model by providing statistically based decision support.