LOCAL LINEAR FORECASTS USING CUBIC SMOOTHING SPLINES

This paper shows how cubic smoothing splines fitted to univariate time series data can be used to obtain local linear forecasts. The approach is based on a stochastic state‐space model which allows the use of likelihoods for estimating the smoothing parameter, and which enables easy construction of prediction intervals. The paper shows that the model is a special case of an ARIMA(0, 2, 2) model; it provides a simple upper bound for the smoothing parameter to ensure an invertible model; and it demonstrates that the spline model is not a special case of Holt's local linear trend method. The paper compares the spline forecasts with Holt's forecasts and those obtained from the full ARIMA(0, 2, 2) model, showing that the restricted parameter space does not impair forecast performance. The advantage of this approach over a full ARIMA(0, 2, 2) model is that it gives a smooth trend estimate as well as a linear forecast function.     

A Bootstrap Test for Circular Data

In this article, variance stabilizing filters are discussed. A new filter with nice properties is proposed which makes use of moving averages and moving standard deviations, the latter smoothed with the Hodrick-Prescott filter. This filter is compared to a GARCH-type filter. An ARIMA model is estimated for the filtered GDP series, and the parameter estimates are used in forecasting the unfiltered series. These forecasts compare well with those of ARIMA, ARFIMA, and GARCH models based on the unfiltered data. The filter does not color white noise.     

The Integration of Artificial Neural Networks and Text Mining to Forecast Gold Futures Prices

Although a previous study found that neural network forecasts were more accurate than time series models for predicting Latin American stock indexes, the forecasting accuracy of neural network for predicting gold futures prices has never been discussed. Therefore, the first objective of this study is to compare the forecasting accuracy of a neural network model with that of ARIMA models. Furthermore, the fluctuations in gold futures are not only influenced by the quantitative variables, but also by many nonquantifiable factors, such as wars, international relations, and terrorist attacks. The second objective of this study is therefore to propose the integration of text mining and an artificial neural network to forecast gold futures prices. The historical gold futures prices from 1999 to 2008 were used as training data and testing data, and the prices of 2009 were used to examine the effectiveness of the proposed model. The results of empirical analysis showed that an artificial neural network forecasted gold futures prices better than ARIMA models did. In addition, text mining provided a reasonable explanation of the trend in gold futures prices.     

Predictive Accuracy Gain From Disaggregate Sampling in ARIMA Models

We compare the forecast accuracy of autoregressive integrated moving average (ARIMA) models based on data observed with high and low frequency, respectively. We discuss how, for instance, a quarterly model can be used to predict one quarter ahead even if only annual data are available, and we compare the variance of the prediction error in this case with the variance if quarterly observations were indeed available. Results on the expected information gain are presented for a number of ARIMA models including models that describe the seasonally adjusted gross national product (GNP) series in the Netherlands. Disaggregation from annual to quarterly GNP data has reduced the variance of short-run forecast errors considerably, but further disaggregation from quarterly to monthly data is found to hardly improve the accuracy of monthly forecasts.     

Effect of systematic sampling on arima models

Given a general homogeneous non-stationary autoregressive integrated moving average process ARIMA(p,d,q), the corresponding model for the subseries obtained by a systematic sampling is derived. The article then shows that the sampled subseries approaches approximately to an integrated moving average process IMA(d,l), l≤(d-l), regardless of the autoregressive and moving average structures in the original series. In particular, the sampled subseries from an ARIMA (p,l,q) process approaches approximately to a simple random walk model.     

Sampling the Future: A Bayesian Approach to Forecasting From Univariate Time Series Models

The Box–Jenkins methodology for modeling and forecasting from univariate time series models has long been considered a standard to which other forecasting techniques have been compared. To a Bayesian statistician, however, the method lacks an important facet—a provision for modeling uncertainty about parameter estimates. We present a technique called sampling the future for including this feature in both the estimation and forecasting stages. Although it is relatively easy to use Bayesian methods to estimate the parameters in an autoregressive integrated moving average (ARIMA) model, there are severe difficulties in producing forecasts from such a model. The multiperiod predictive density does not have a convenient closed form, so approximations are needed. In this article, exact Bayesian forecasting is approximated by simulating the joint predictive distribution. First, parameter sets are randomly generated from the joint posterior distribution. These are then used to simulate future paths of the time series. This bundle of many possible realizations is used to project the future in several ways. Highest probability forecast regions are formed and portrayed with computer graphics. The predictive density's shape is explored. Finally, we discuss a method that allows the analyst to subjectively modify the posterior distribution on the parameters and produce alternate forecasts.     

Random Level-Shift Time Series Models,ARIMA Approximations,and Level-Shift Detection

The main purpose of this article is to assess the performance of autoregressive integrated moving average (ARIMA) models when occasional level shifts occur in the time series under study. A random level-shift time series model that allows the level of the process to change occasionally is introduced. Between two consecutive changes, the process behaves like the usual autoregressive moving average (ARMA) process. In practice, a series generated from a random level-shift ARMA (RLARMA) model may be misspecified as an ARIMA process. The efficiency of this ARIMA approximation with respect to estimation of current level and forecasting is investigated. The results of examining a special case of an RLARMA model indicate that the ARIMA approximations are inadequate for estimating the current level, but they are robust for forecasting future observations except when there is a very low frequency of level shifts or when the series are highly negatively correlated. A level-shift detection procedure is presented to handle the low-frequency level-shift phenomena, and its usefulness in building models for forecasting is demonstrated.     

Birth forecasting based on birth order probabilities,with application to U.S. data

"A model for birth forecasting based on prediction of the so-called 'birth order probabilities' is constructed. The relation between this model and recent models of fertility prediction is derived. Birth forecasts with approximate probability limits for the U.S. for the period 1983-1997 are generated. The performance of the proposed model in predicting future fertility is tested by fitting time series models to part of the available series (1917-1982) and ultimately generating birth forecasts for the remainder of the period, then comparing these forecasts with the actual data." The accuracy of the fertility forecasts made are compared with those made by other methods.     

Predicting daily highs and lows of exchange rates: a cointegration analysis

This article presents empirical evidence that links the daily highs and lows of exchange rates of the US dollar against two other major currencies over a 15 year period. We find that the log high and log low of an exchange rate are cointegrated, and the error correction term is well-approximated by the range, which is defined as the difference between the log high and log low. We further assess the empirical relevance of jointly analyzing the highs, lows and the ranges by comparing the range forecasts generated from the cointegration framework with those from random walk and autoregressive integrated moving average (ARIMA) specifications. The ability of range forecasts as predictors of implied volatility for a European style currency option is also evaluated. Our results show that aside from a limited set of exceptions, the cointegration framework generally outperforms the random walk and ARIMA models in an out-of-sample forecast contest.     

Fractionally integrated ARMA for crude palm oil prices prediction: case of potentially overdifference

Dealing with stationarity remains an unsolved problem. Some of the time series data, especially crude palm oil (CPO) prices persist towards nonstationarity in the long-run data. This dilemma forces the researchers to conduct first-order difference. The basic idea is that to obtain the stationary data that is considered as a good strategy to overcome the nonstationary counterparts. An opportune remark as it is, this proxy may lead to overdifference. The CPO prices trend elements have not been attenuated but nearly annihilated. Therefore, this paper presents the usefulness of autoregressive fractionally integrated moving average (ARFIMA) model as the solution towards the nonstationary persistency of CPO prices in the long-run data. In this study, we employed daily historical Free-on-Board CPO prices in Malaysia. A comparison was made between the ARFIMA over the existing autoregressive-integrated moving average (ARIMA) model. Here, we employed three statistical evaluation criteria in order to measure the performance of the applied models. The general conclusion that can be derived from this paper is that the usefulness of the ARFIMA model outperformed the existing ARIMA model.     

Forecasting Economic Time Series With Structural and Box-Jenkins Models: A Case Study

The basic structural model is a univariate time series model consisting of a slowly changing trend component, a slowly changing seasonal component, and a random irregular component. It is part of a class of models that have a number of advantages over the seasonal ARIMA models adopted by Box and Jenkins (1976). This article reports the results of an exercise in which the basic structural model was estimated for six U.K. macroeconomic time series and the forecasting performance compared with that of ARIMA models previously fitted by Prothero and Wallis (1976).     

基于均衡关系的中国人口死亡率预测模型

人口死亡率反映了人口的死亡程度,准确预测死亡率是人口科学及人口经济学研究的重点之一,同时也是长寿风险测量的重要数据基础。基于Lee-Carter模型,探索中国大陆与台湾地区死亡率的相关性,通过协整分析考虑两地死亡率的长期均衡关系,创新性地建立基于相关性的向量误差修正模型(VECM),克服传统自回归移动平均模型(ARIMA)使用有限数据进行预测的局限性;均方预测误差作为检验标准,结果表明:基于VECM模型的预测效果比传统的预测效果更佳;基于中国大陆地区和台湾地区的死亡率长期均衡关系,可以为两地联合长寿债券的定价提供重要参考。     

Statistical analysis of error for fourth-order ordinary differential equation solvers

We develop an autoregressive integrated moving average (ARIMA) model to study the statistical behavior of the numerical error generated from three fourth-order ordinary differential equation solvers: Milne's method, Adams–Bashforth method and a new method that randomly switches between the Milne and Adams–Bashforth methods. With the actual error data based on three differential equations, we desire to identify an ARIMA model for each data series. Results show that some of the data series can be described by ARIMA models but others cannot. Based on the mathematical form of the numerical error, other statistical models should be investigated in the future. Finally, we assess the multivariate normality of the sample mean error generated by the switching method.     

Stochastic modelling of regional annual rainfall anomalies in East Africa

ARIMA (p, d, q) models were fitted to areal annual rainfall of two homogeneous regions in East Africa with rainfall records extending between the period 1922–80. The areal estimates of the regional rainfall were derived from the time series of the first eigenvector, which was significantly dominant at each of the two regions. The first eigenvector accounted for about 80% of the total rainfall variance in each region.

The class of ARIMA (p, d, q) models which best fitted the areal indices of relative wetness/dryness were the A R M A (3, 1) models. Tests of forecasting skill however indicated low skill in the forecasts given by these models. In all cases the models accounted for less than 50% of the total variance.

Spectral analysis of the indices time series indicated dominant quasi-periodic fluctuations around 2.2–2.8 years, 3–3.7 years, 5–6 years and 10–13 years. These spectral bands however accounted for very low proportion of the total rainfall variance.     

Exact joint forecast regions for vector autoregressive models

Assume that a k-element vector time series follows a vector autoregressive (VAR) model. Obtaining simultaneous forecasts of the k elements of the vector time series is an important problem. Based on the Bonferroni inequality, Lutkepohl (1991) derived the procedures which construct the conservative joint forecast regions for the VAR model. In this paper, we propose to use an exact method which provides shorter prediction intervals than does the Bonferroni method. Three illustrative examples are given for comparison of the various VAR forecasting procedures.     

Temporal disaggregation and restricted forecasting of multiple population time series

This article presents some applications of time-series procedures to solve two typical problems that arise when analyzing demographic information in developing countries: (1) unavailability of annual time series of population growth rates (PGRs) and their corresponding population time series and (2) inappropriately defined population growth goals in official population programs. These problems are considered as situations that require combining information of population time series. Firstly, we suggest the use of temporal disaggregation techniques to combine census data with vital statistics information in order to estimate annual PGRs. Secondly, we apply multiple restricted forecasting to combine the official targets on future PGRs with the disaggregated series. Then, we propose a mechanism to evaluate the compatibility of the demographic goals with the annual data. We apply the aforementioned procedures to data of the Mexico City Metropolitan Zone divided by concentric rings and conclude that the targets established in the official program are not feasible. Hence, we derive future PGRs that are both in line with the official targets and with the historical demographic behavior. We conclude that growth population programs should be based on this kind of analysis to be supported empirically. So, through specialized multivariate time-series techniques, we propose to obtain first an optimal estimate of a disaggregate vector of population time series and then, produce restricted forecasts in agreement with some data-based population policies here derived.     

A Review of Some Modern Approaches to the Problem of Trend Extraction

This article presents a review of some modern approaches to trend extraction for one-dimensional time series, which is one of the major tasks of time series analysis. The trend of a time series is usually defined as a smooth additive component which contains information about the time series global change, and we discuss this and other definitions of the trend. We do not aim to review all the novel approaches, but rather to observe the problem from different viewpoints and from different areas of expertise. The article contributes to understanding the concept of a trend and the problem of its extraction. We present an overview of advantages and disadvantages of the approaches under consideration, which are: the model-based approach (MBA), nonparametric linear filtering, singular spectrum analysis (SSA), and wavelets. The MBA assumes the specification of a stochastic time series model, which is usually either an autoregressive integrated moving average (ARIMA) model or a state space model. The nonparametric filtering methods do not require specification of model and are popular because of their simplicity in application. We discuss the Henderson, LOESS, and Hodrick–Prescott filters and their versions derived by exploiting the Reproducing Kernel Hilbert Space methodology. In addition to these prominent approaches, we consider SSA and wavelet methods. SSA is widespread in the geosciences; its algorithm is similar to that of principal components analysis, but SSA is applied to time series. Wavelet methods are the de facto standard for denoising in signal procession, and recent works revealed their potential in trend analysis.     

The Seasonal Adjustment Procedures for the Consumer Price Indexes: Some Empirical Results

Beginning with January of 1987, the consumer price indexes (CPI's) have been seasonally adjusted by the X-11 autoregressive integrated moving average (ARIMA) procedure. This modification of the X-11 procedure was introduced following an empirical investigation into three aspects of seasonal adjustment methodology as applied to several CPI series—the choice of ARIMA models to fit and forecast those series, the improvements made by the ARIMA modification in terms of revision and smoothness of the seasonally adjusted series, and the effect on the quality of seasonal adjustment and the identifiability of seasonality due to the ARIMA modification. This article reports the results of that investigation, in addition, a brief account is given of the U.S. Bureau of Labor Statistics procedures relating to the projected seasonal factors, seasonally adjusted aggregate series, and the revisions of the seasonally adjusted series.     

基于传递函数的产品价格预测模型

对多变量时间序列进行预测,单变量ARIMA模型和普通多元回归分析并不适用,这种情况下应用多变量ARIMA即传递函数模型是很好的选择。以一种受原油和原材料多种因素影响的合成化纤产品为例,说明利用传递函数模型对其价格进行预测的建模过程中,如何进行模型识别、参数估计及诊断的有关问题。     

Selection between models through multi-step-ahead forecasting

We develop and show applications of two new test statistics for deciding if one ARIMA model provides significantly better h-step-ahead forecasts than another, as measured by the difference of approximations to their asymptotic mean square forecast errors. The two statistics differ in the variance estimates used for normalization. Both variance estimates are consistent even when the models considered are incorrect. Our main variance estimate is further distinguished by accounting for parameter estimation, while the simpler variance estimate treats parameters as fixed. Their broad consistency properties offer improvements to what are known as tests of Diebold and Mariano (1995) type, which are tests that treat parameters as fixed and use variance estimates that are generally not consistent in our context. We show how these statistics can be calculated for any pair of ARIMA models with the same differencing operator.