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This study aims to predict overnight stays in Italy at tourist accommodation facilities through a nonlinear, single factor, stochastic model called CIR#. The contribution of this study is twofold: in terms of forecast accuracy and in terms of parsimony (both from the perspective of the data and the complexity of the modeling), especially when a regular pattern in the time series is disrupted. This study shows that the CIR# not only performs better than the considered baseline models but also has a much lower error than other additional models or approaches reported in the literature.

Typically, tourism demand tends to follow regular trends, such as low and high seasons on a quarterly/monthly level and weekends and holidays on a daily level. The data set consists of nights spent in Italy at tourist accommodation establishments as collected on a monthly basis by Eurostat before and during the COVID-19 pandemic breaking regular patterns.

Traditional tourism demand forecasting models may face challenges when massive amounts of search intensity indices are adopted as tourism demand indicators. In addition, given the importance of accurate forecasts, many studies have proposed novel hybrid models or used various combinations of methods. Thus, although there are clear benefits in adopting more complex approaches, the risk is that of dealing with unwieldy models. To demonstrate how this approach can be fruitfully extended to tourism, the accuracy of the CIR# is tested by using standard metrics such as root mean squared errors, mean absolute errors, mean absolute percentage error or average relative mean squared error.

The CIR# model is notably simpler than other models found in literature and does not rely on black box techniques such as those used in neural network (NN) or data science-based models. The carried analysis suggests that the CIR# model outperforms other reference predictions in terms of statistical significance of the error.

The proposed model stands out for being a viable option to the Holt–Winters (HW) model, particularly when dealing with irregular data.

The proposed model has demonstrated superiority even when compared to other models in the literature, and it can be especially useful for tourism stakeholders when making decisions in the presence of disruptions in data patterns.

The novelty lies in the fact that the proposed model is a valid alternative to the HW, especially when the data are not regular. In addition, compared to many existing models in the literature, the CIR# model is notably simpler and more transparent, avoiding the “black box” nature of NN and data science-based models.

一般来说, 旅游需求往往遵循规律的趋势, 例如季度/月的淡季和旺季, 以及日常的周末和假期。该数据集包括欧盟统计局在打破常规模式的2019冠状病毒病大流行之前和期间每月收集的在意大利旅游住宿设施度过的夜晚。

本研究旨在通过一个名为cir#的非线性单因素随机模型来预测意大利游客住宿设施的过夜住宿情况。这项研究的贡献是双重的:在预测准确性方面和在简洁方面(从数据和建模复杂性的角度来看), 特别是当时间序列中的规则模式被打乱时。我们表明, cir#不仅比考虑的基线模型表现更好, 而且比文献中报告的其他模型或方法具有更低的误差。

当大量搜索强度指标被作为旅游需求指标时, 传统的旅游需求预测模型将面临挑战。此外, 鉴于准确预测的重要性, 许多研究提出了新的混合模型或使用各种方法的组合。因此, 尽管采用更复杂的方法有明显的好处, 但风险在于处理难使用的模型。为了证明这种方法能有效地扩展到旅游业, 使用RMSE、MAE、MAPE或AvgReIMSE等标准指标来测试cir#的准确性。

cir#模型明显比文献中发现的其他模型简单, 并且不依赖于黑盒技术, 例如在神经网络或基于数据科学的模型中使用的技术。所进行的分析表明, cir#模型在误差的统计显著性方面优于其他参考预测。

这个模型作为Holt-Winters模型的一个拟议模型, 特别是在处理不规则数据时。

即使与文献中的其他模型相比, 所提出的模型也显示出优越性, 并且在数据模式中断时对旅游利益相关者做出决策特别有用。

创新之处在于所提出的模型是Holt-Winters模型的有效替代方案, 特别是当数据不规律时。此外, 与文献中的许多现有模型相比, cir#模型明显更简单、更透明, 避免了神经网络和基于数据科学的模型的“黑箱”性质。

Normalmente, la demanda turística tiende a seguir tendencias regulares, como temporadas altas y bajas a nivel trimestral/mensual y fines de semana y festivos a nivel diario. El conjunto de datos consiste en las pernoctaciones en Italia en establecimientos de alojamiento turístico recogidas mensualmente por Eurostat antes y durante la pandemia de COVID-19, rompiendo los patrones regulares.

El presente estudio pretende predecir las pernoctaciones en Italia en establecimientos de alojamiento turístico mediante un modelo estocástico no lineal de un solo factor denominado CIR#. La contribución de este estudio es doble: en términos de precisión de la predicción y en términos de parsimonia (tanto desde la perspectiva de los datos como de la complejidad de la modelización), especialmente cuando un patrón regular en la serie temporal se ve interrumpido. Demostramos que el CIR# no sólo aplica mejor que los modelos de referencia considerados, sino que también tiene un error mucho menor que otros modelos o enfoques adicionales de los que se informa en la literatura.

Los modelos tradicionales de previsión de la demanda turística pueden enfrentarse a desafíos cuando se adoptan cantidades masivas de índices de intensidad de búsqueda como indicadores de la demanda turística. Además, dada la importancia de unas previsiones precisas, muchos estudios han propuesto modelos híbridos novedosos o han utilizado diversas combinaciones de métodos. Así pues, aunque la adopción de enfoques más complejos presenta ventajas evidentes, el riesgo es el de enfrentarse a modelos poco manejables. Para demostrar cómo este enfoque puede extenderse de forma fructífera al turismo, se comprueba la precisión del CIR# utilizando métricas estándar como RMSE, MAE, MAPE o AvgReIMSE.

El modelo CIR# es notablemente más sencillo que otros modelos encontrados en la literatura y no se basa en técnicas de caja negra como las utilizadas en los modelos basados en redes neuronales o en la ciencia de datos. El análisis realizado sugiere que el modelo CIR# supera a otras predicciones de referencia en términos de significación estadística del error.

El modelo propuesto destaca por ser una opción viable al modelo Holt-Winters, sobre todo cuando se trata de datos irregulares.

El modelo propuesto ha demostrado su superioridad incluso cuando se compara con otros modelos de la bibliografía, y puede ser especialmente útil para los agentes del sector turístico a la hora de tomar decisiones cuando se producen alteraciones en los patrones de datos.

La novedad radica en que el modelo propuesto es una alternativa válida al Holt-Winters especialmente cuando los datos no son regulares. Además, en comparación con muchos modelos existentes en la literatura, el modelo CIR# es notablemente más sencillo y transparente, evitando la naturaleza de “caja negra” de los modelos basados en redes neuronales y en ciencia de datos.

The purpose of this study is to suggest a new framework that we call the CIR#, which allows forecasting interest rates from observed financial market data even when rates are negative. In doing so, we have the objective is to maintain the market volatility structure as well as the analytical tractability of the original CIR model.

The novelty of the proposed methodology consists in using the CIR model to forecast the evolution of interest rates by an appropriate partitioning of the data sample and calibration. The latter is performed by replacing the standard Brownian motion process in the random term of the model with normally distributed standardized residuals of the “optimal” autoregressive integrated moving average (ARIMA) model.

The suggested model is quite powerful for the following reasons. First, the historical market data sample is partitioned into sub-groups to capture all the statistically significant changes of variance in the interest rates. An appropriate translation of market rates to positive values was included in the procedure to overcome the issue of negative/near-to-zero values. Second, this study has introduced a new way of calibrating the CIR model parameters to each sub-group partitioning the actual historical data. The standard Brownian motion process in the random part of the model is replaced with normally distributed standardized residuals of the “optimal” ARIMA model suitably chosen for each sub-group. As a result, exact CIR fitted values to the observed market data are calculated and the computational cost of the numerical procedure is considerably reduced. Third, this work shows that the CIR model is efficient and able to follow very closely the structure of market interest rates (especially for short maturities that, notoriously, are very difficult to handle) and to predict future interest rates better than the original CIR model. As a measure of goodness of fit, this study obtained high values of the statistics R² and small values of the root of the mean square error for each sub-group and the entire data sample.

A limitation is related to the specific dataset as we are examining the period around the 2008 financial crisis for about 5 years and by using monthly data. Future research will show the predictive power of the model by extending the dataset in terms of frequency and size.

Improved ability to model/forecast interest rates.

The original value consists in turning the CIR from modeling instantaneous spot rates to forecasting any rate of the yield curve.

The purpose of this paper is to model interest rates from observed financial market data through a new approach to the Cox–Ingersoll–Ross (CIR) model. This model is popular among financial institutions mainly because it is a rather simple (uni-factorial) and better model than the former Vasicek framework. However, there are a number of issues in describing interest rate dynamics within the CIR framework on which focus should be placed. Therefore, a new methodology has been proposed that allows forecasting future expected interest rates from observed financial market data by preserving the structure of the original CIR model, even with negative interest rates. The performance of the new approach, tested on monthly-recorded interest rates data, provides a good fit to current data for different term structures.

To ensure a fitting close to current interest rates, the innovative step in the proposed procedure consists in partitioning the entire available market data sample, usually showing a mixture of probability distributions of the same type, in a suitable number of sub-sample having a normal/gamma distribution. An appropriate translation of market interest rates to positive values has been introduced to overcome the issue of negative/near-to-zero values. Then, the CIR model parameters have been calibrated to the shifted market interest rates and simulated the expected values of interest rates by a Monte Carlo discretization scheme. We have analysed the empirical performance of the proposed methodology for two different monthly-recorded EUR data samples in a money market and a long-term data set, respectively.

Better results are shown in terms of the root mean square error when a segmentation of the data sample in normally distributed sub-samples is considered. After assessing the accuracy of the proposed procedure, the implemented algorithm was applied to forecast next-month expected interest rates over a historical period of 12 months (fixed window). Through an error analysis, it was observed that our algorithm provides a better fitting of the predicted expected interest rates to market data than the exponentially weighted moving average model. A further confirmation of the efficiency of the proposed algorithm and of the quality of the calibration of the CIR parameters to the observed market interest rates is given by applying the proposed forecasting technique.

This paper has the objective of modelling interest rates from observed financial market data through a new approach to the CIR model. This model is popular among financial institutions mainly because it is a rather simple (uni-factorial) and better model than the former Vasicek model (Section 2). However, there are a number of issues in describing short-term interest rate dynamics within the CIR framework on which focus should be placed. A new methodology has been proposed that allows us to forecast future expected short-term interest rates from observed financial market data by preserving the structure of the original CIR model. The performance of the new approach, tested on monthly data, provides a good fit for different term structures. It is shown how the proposed methodology overcomes both the usual challenges (e.g. simulating regime switching, clustered volatility and skewed tails), as well as the new ones added by the current market environment (particularly the need to model a downward trend to negative interest rates).