Quantile Regression Neural Network Model For Forecasting Consumer Price Index In Indonesia

The main purpose of time series analysis is to obtain the forecasting result from an observation for future values. Quantile Regression Neural Network is a statistical method that can model data with non-homogeneous variance with artificial neural network approach that can capture nonlinear patterns in the data. Real data that allegedly have such characteristics is Consumer Price Index (CPI).  CPI forecasting is important to assess price changes associated with cost of living as well as identifying periods of inflation or deflation. The purpose of this research is to compare several method of forecasting CPI in Indonesia. The data used in this study during January 2007 until April 2018 period. QRNN method will be compared with Neural Network with RMSE evaluation criteria. The result is QRNN is the best method for forecasting CPI with RMSE 0.95

Encountered Problems of Time Series with Neural Networks: Models and Architectures

The growing interest in the development of forecasting applications with neural networks is denoted by the publication of more than 10,000 research articles present in the literature. However, the high number of factors included in the configuration of the network, the training process, validation and forecasting, and the sample of data, which must be determined in order to achieve an adequate network model for forecasting, converts neural networks in an unstable technique, given that any change in training or in some parameter produces great changes in the prediction. In this chapter, an analysis of the problematic around the factors that affect the construction of the neural network models is made and that often present inconsistent results, and the fields that require additional research are highlighted

A review and comparison of strategies for multi-step ahead time series forecasting based on the NN5 forecasting competition

Multi-step ahead forecasting is still an open challenge in time series forecasting. Several approaches that deal with this complex problem have been proposed in the literature but an extensive comparison on a large number of tasks is still missing. This paper aims to fill this gap by reviewing existing strategies for multi-step ahead forecasting and comparing them in theoretical and practical terms. To attain such an objective, we performed a large scale comparison of these different strategies using a large experimental benchmark (namely the 111 series from the NN5 forecasting competition). In addition, we considered the effects of deseasonalization, input variable selection, and forecast combination on these strategies and on multi-step ahead forecasting at large. The following three findings appear to be consistently supported by the experimental results: Multiple-Output strategies are the best performing approaches, deseasonalization leads to uniformly improved forecast accuracy, and input selection is more effective when performed in conjunction with deseasonalization

Input-variable Specification for Neural Networks - an Analysis of Forecasting low and high Time Series Frequency

Prior research in forecasting time series with Neural Networks (NN) has provided inconsistent evidence on their predictive accuracy. In management, NN have shown only inferior performance on well established benchmark time series of monthly, quarterly or annual frequency. In contrast, NN have shown preeminent accuracy in electrical load forecasting on daily or hourly time series, leading to successful real life applications. While this inconsistency has been traditionally attributed to the lack of a reliable methodology to model NNs, recent research indicates that the particular data properties of high frequency time series may be equally important. High frequency time series of daily, hourly or even shorter time intervals pose additional modelling challenges in the length and structure of the time series, which may abet the use of novel methods. This analysis aims to identify and contrast the challenges in modelling NN for low and high frequency data in order to develop a unifying forecasting methodology tailored to the properties of the dataset. We conduct a set of experiments in three different frequency domains of daily, weekly and monthly data of one empirical time series of cash machine withdrawals, using a consistent modelling procedure. While our analysis provides evidence that NN are suitable to predict high frequency data, it also identifies a set of challenges in modelling NN that arise from high frequency data, in particular in specifying the input vector, and that require specific modelling approaches applicable to both low and high frequency data

Una nueva metodología de entrenamiento de redes neuronales y sus implicaciones en la selección de modelos

La predicción de series de tiempo con redes neuronales ha sido una práctica aceptada en la literatura, gracias a las bondades de generalización y ajuste que poseen dichos modelos; sin embargo, el elevado número de factores que deben ser determinados en el proceso de construcción de un modelo de redes neuronales, a menudo, conduce a resultados inconsistentes puesto que depende en muchas instancias de las decisiones tomadas por el modelador(Zhang et al., 1998).La capacidad de ajuste de una red neuronal se ve afectada por la configuración usada, en especial, en relación al número de neuronas ocultas y de variables de entrada, toda vez que, a medida que el número de parámetros del modelo aumenta, se favorece el aprendizaje de la red y por tanto el ajuste es mejor. En teoría, un proceso iterativo de adición de parámetros (entradas y neuronas ocultas) debería conducir a reducciones sistemáticas en el error de ajuste. En esta tesis se validó la hipótesis que la adición de entradas y neuronas ocultas debe conducir a reducciones en el error de ajuste, donde la evidencia experimental demostró que los métodos de optimización evaluados exhiben comportamientos diferentes a los teóricamente esperados, incumpliendo el supuesto de reducción del error. Por lo tanto, el logro principal de esta tesis es el desarrollo una estrategia para la construcción de modelos de red neuronal basada en el diseño de un algoritmo de entrenamiento que garantice la reducción del error de ajuste a medida que se agregan parámetros a la red neuronal. Para cumplir con el criterio de reducción del error de ajuste, se diseñó una estrategia constructiva orientada a conservar, en el nuevo modelo, los pesos de los parámetros del modelo anterior (modelo con menos neuronas o entradas) y hacer cero los pesos de las nuevas conexiones, como un paso previo a la optimización del modelo. La optimización del nuevo modelo parte del valor de error alcanzado por el modelo anterior y, por lo tanto, debe mejorar o permanecer igual. La aplicación experimental de la estrategia constructiva presenta resultados ampliamente satisfactorios, toda vez que, no sólo se cumple con la reducción del error, sino que se alcanzar valores con precisión cero en el error de ajuste. Igualmente, se desarrollaron modificaciones a la estrategia constructiva de tal forma que se pueda reducir el número de modelos que se requieren evaluar. En este punto se realizaron dos modificaciones, una considerando la adición de entradas de forma secuencial (ordenada), y otra de forma no secuencial. Para lograr la reducción en el número de modelos evaluados, en la estrategia secuencial para cada nuevo modelo se contrastan si debe adicionarse una entrada o una neurona; la decisión se toma basada en el menor error de ajuste. La estrategia no secuencial permite que entradas no contiguas puedan incluirse en la red, de tal forma que, la decisión de incluir una neurona oculta o una entrada, implica evaluar el error de ajuste de todas las entradas disponibles; el nuevo modelo es aquel que aporte mayor beneficio en el error del modelo. Los resultados experimentales satisfacen ampliamente el requerimiento, toda vez que se alcanzan reducciones muy significativas en el número de modelos a evaluar con el uso de ambas estrategias. Posteriormente, se evalúa el impacto de la estrategia constructiva planteada sobre tres categorías de criterios de selección o especificación del modelo: basados en error de ajuste, en criterios de información, y en pruebas estadísticas. La selección basada en las estrategias de especificación de modelos indica que dichos criterios no están en capacidad de elegir el mejor modelo tras contar con un algoritmo constructivo consistente., por lo tanto, carecen de validez. Los resultados encontrados impactan fuertemente los procesos de construcción y especificación de modelos de redes neuronales, toda vez que, conducen a tener modelos sobre-parametrizados con una alta tendencia al sobre-ajuste, lo que se traduce en modelo con muy buen ajuste, pero con pobre generalización y baja parsimonia. Los principales aportes de esta tesis son cuatro: La validación de la hipótesis que la adición iterativa de neuronas ocultas y entradas en un modelo de redes neuronales debe conducir a reducciones en el error de ajuste, y la discusión de sus implicaciones. El desarrollo una estrategia para la construcción de modelos de red neuronal basada en el diseño de un algoritmo de entrenamiento que garantiza la reducción del error de ajuste a medida que se agregan parámetros a la red neuronal. El desarrollo de dos estrategias constructivas modificadas que permiten reducir el número de modelos que se requieren evaluar; una donde las entradas se agregan de forma secuencial y otra, no secuencial. La evaluación de la estrategia constructiva planteada sobre los criterios de selección del modelo /Abstract. Time series prediction with neural networks has been an accepted practice in the literature, for its high ability of generalization and adjustment, however, the large number of factors must be determined in the building a neural network model often leads to inconsistent results since it depends on many instances of decisions made by the modeler (Zhang et al., 1998). Adjustment capacity of a neural network is affected by the configuration used, especially by the number of hidden neurons and input variables. When the number of model parameters increases, improves learning network and therefore the setting is best. In theory, an iterative process of adding parameters (inputs and hidden neurons) should lead to systematic reductions in adjustment error. This thesis validated the hypothesis that addition of inputs and hidden neurons should lead to reductions in the adjustment error. Experimental evidence showed that the optimization methods exhibit different behaviors to the theoretically expected; therefore, the models fail in the reduction assumption of adjustment error. The main achievement of this thesis is the developing a strategy for building neural network models based on the design of a training algorithm that ensures error reduction when added parameters to the neural network. To achieve the reduction assumption of adjustment error, we designed a constructive strategy aimed at conserving the weights of the parameters of the previous model (model with fewer neurons or inputs) and to zero the weights of the new connections, prior to the optimization of the model. The optimization of the new model retains the error value reached by the previous model and, therefore, be improved or remain the same. The experimental application of the constructive approach presented results widely satisfactory, because complies with the reduction of error, and permit to reach values near to zero in the adjustment error. Likewise, we did modifications the constructive strategy so that it can reduce the model numbers that require evaluation. Two modifications were made, one considering adding entries sequentially (ordinate), and other non-sequential. To achieve a reduction in the number of models tested, in the sequential strategy each new model is compared if should be added an entry or a neuron, the decision is based on the lowest adjustment error. The non-sequential strategy allows non-contiguous entries may be included in the network, so that the decision to include a hidden neuron or input involves evaluate all entries available; the new model is one that provides greater reduction in the error. The experimental results fully satisfy the requirements; they achieve very significant reductions in the number of model to evaluate using both strategies. Subsequently, we evaluate the impact of the constructive strategy on three categories of selection criteria or specification of the model: based on adjustment error, in information criteria, and statistical tests. Selection based on the strategies of model specification indicates that none of these criteria are not able to choose the best model, therefore, these strategies are not valid. The results strongly impact the processes of building and specification of neural network models, since, leading to over-parameterized models have a high tendency to over-adjustment, which results in very good model fit, but with poor generalization and low parsimony. The main contributions of this this are four: Validation of the hypothesis that the iterative addition of hidden neurons and inputs in a neural network model should lead to reductions in the fit error, and discussion of its implications. Developing a strategy for building neural network models based on the design of a training algorithm that ensures error reduction when are added parameters to the neural network. Development of two modified constructive strategies that reduce the number of models that require evaluation, one where the inputs are added sequentially and the other, non-sequential. Evaluation of the performance of constructive strategies by model selection criteriaDoctorad

Aplikasi Model Hybrid Quantile Regression Neural Network pada Peramalan Pecahan Inflow dan Outflow Uang Kartal di Indonesia

Regresi kuantil merupakan perluasan dari regresi Ordinary Least Square (OLS) yang dapat menjelaskan keterkaitan antar variabel pada berbagai kuantil. Regresi kuantil juga dapat digunakan dalam peramalan data runtun waktu. Penelitian ini bertujuan untuk memperoleh model peramalan inflow dan outflow tiap pecahan di Indonesia yang akurat dan dapat menangkap pola variasi kalender serta heteroskedastisitas. Untuk meningkatkan akurasi hasil peramalan, regresi kuantil dikombinasikan dengan neural network, yang dikenal sebagai quantile regression neural network (QRNN). Metode QRNN akan dibandingkan dengan metode ARIMAX dan neural network berdasarkan RMSE, MAE, MdAE, MAPE, dan MdAPE. Terdapat dua kajian dalam penelitian ini, yakni studi simulasi dan aplikasi pada 14 pecahan data inflow dan outflow di Indonesia. Studi simulasi menunjukkan bahwa QRNN dapat menangkap pola heteroskedastisitas dan nonlinieritas dibandingkan ARIMAX dan neural network. Sedangkan aplikasi pada data inflow dan outflow menunjukkan bahwa QRNN merupakan metode terbaik dalam meramalkan 10 dari 14 pecahan. Namun peramalan interval metode QRNN menunjukkan adanya crossing antar kuantil yang disebabkan oleh pengestimasian kuantil secara independen. ================================================================= Quantile regression was developed from Ordinary Least Square regression. Furthermore, quantile regression can explain the relationship between variables on various quantiles. Quantile regression can be applied in forecasting analysis. The aim of this study was to find the best model for forecasting inflow and outflow in Indonesia which can overcome heteroscedasticity and nonlinearity problem. In order to improve the accuracy of forecasting results, quantile regression will be combined with neural network method, known as quantile regression neural network (QRNN). QRNN will be compared with ARIMAX and neural network method based on RMSE, MAE, MdAE, MAPE, and MdAPE criteria. In this study, there are two main topics will be discussed, i.e simulation study and case study about 14 currencies of inflow and outflow data. Simulation study shows that QRNN is the best method to solve heteroscedasticity and nonlinearity problem. While, application in inflow and outflow data shows that QRNN is the best method to forecast 10 of 14 currencies. However, there is a crossing within quantile which can be caused by the estimates of each quantile that are calculated independently

Model Hybrid GSTARX-ANN Untuk Peramalan Data Space-Time Dengan Efek Variasi Kalender (Studi Kasus : Data Inflow Dan Outflow Uang Kartal Di Bank Indonesia Wilayah Jawa Timur)

Selain berdimensi waktu, data juga bisa berdimensi ruang yang dikenal dengan data space-time. Model space-time merupakan suatu model yang menggabungkan unsur dependensi waktu dan lokasi pada suatu data time series multivariat, salah satu model space-time adalah Generalized Space-Time Autoregressive (GSTAR). Model GSTAR memiliki keterbatasan yaitu tidak mampu memodelkan time series yang nonlinier, namun hal ini bisa diatasi dengan menerapkan model hybrid pada GSTAR. Pada penelitian ini akan dilakukan pemodelan hybrid GSTARX-ANN, dimana model GSTARX sebagai komponen linier yang melibatkan variabel prediktor, yaitu efek variasi kalender dan ANN sebagai komponen nonlinier. Model hybrid GSTARX-ANN merupakan model terbaik dalam meramalkan data simulasi yang mengandung komponen tren, musiman, variasi kalender, dan deret noise linier maupun nonlinier dibandingkan model VARX dan GSTARX. Data inflow dan outflow di KPw BI wilayah Jawa Timur dipengaruhi oleh tren kebijakan BI, musiman, dan variasi kalender, serta mengandung unsur nonlinearity. Pengaruh minggu terjadinya hari raya Idul Fitri juga berpengaruh terhadap tingginya inflow dan outflow. Pada pemodelan data inflow di KPw BI wilayah Jawa Timur, model GSTARX-FFNN(8,2,1) bobot invers jarak merupakan model terbaik, sedangkan pada pemodelan data outflow model GSTARX-FFNN(8,15,1) merupakan model terbaik. ================================================================================================================== Aside from time dimension, data can also dimension of space known as space-time data. The space-time model is a model that combines elements of time and location dependencies in a multivariate time-series data. One of the space-time models is Generalized Space -Time Autoregressive (GSTAR). The GSTAR model has its limitations of not being able for modeling a nonlinear time series, this can be overcome by applying hybrid model on GSTAR. In this research will be modeling hybrid GSTARX-ANN, where GSTARX model as a linear component involving predictor variable, that is an effect of calendar variation and ANN as a nonlinear component. The hybrid GSTARX-ANN model is the best model for predicting simulation data containing trend, seasonality, calendar variations, linear and nonlinear noise series compared to VARX and GSTARX models. Inflow and outflow data in Bank Indonesia East Java region are influenced by BI policy, seasonal trend, calendar variation, and contain nonlinearity elements. GSTARX-FFNN (8,2,1) is the best model for modeling inflow data in Bank Indonesia East Java region , while GSTARX-FFNN (8,15,1) is the best model for modeling outflow data