Forecasting Shanghai containerized freight index by using time series models

Recently, the container shipping industry has become unpredictable due to volatility and major events affecting the maritime sector. At the same time, approaches to estimating container freight rates using econometric and time series modelling have become very important. Therefore, in this paper, different time-series models have been explored that are related to the Shanghai Containerized Freight Index (SCFI). SMA, EWMA, and, SES, Holt Winter method are used to describe the data and model. Afterward, the Holt Winter method and SARIMA was applied to model and predict the SCFI index. MAPE, RMSE, AIC, BIC are used to measure the performances of the models and predictions. We observe that the SARIMA model provides comparatively better results than the existing freight rate forecasting models while performing short-term forecasts on a monthly rate. Results demonstrate that the increase will continue without losing momentum. Please cite this paper as follows: Koyuncu, K., & Tavacıoğlu, L. (2021). Forecasting Shanghai containerized freight index by using time series models. Marine Science and Technology Bulletin, 10(4), 426-434. https://doi.org/10.33714/masteb.1024663


Introduction
Nowadays, more and more companies are looking for driven decision-makers. Maritime industry intelligence and analytics departments and business managers have to regularly make forecasts of product sales, inventory, requirements, shipment rates, etc. Then, take strategic decisions based on these forecast values. For example, retail stores forecast sales. * Corresponding author E-mail address: tavaciog@itu.edu.tr (L. Tavacıoğlu) They use data of the consumers' past purchases and try to forecast sales for the coming days. Similarly, energy companies forecast production demand of reserves, and price forecast of reserves are used to determine long-term investment plans whereas demand forecasts are used for short-term production planning and competitive pricing. Banks and lending institutions forecast new home purchases and venture capital firms forecast market potential to evaluate business plans. The maritime industries operate in complex global markets and businesses are subject to external forces and constant environmental change. The ability to read, understand and respond effectively to the range of rapidly moving components that make up a market is essential to the modern company's survival. Forecasting is vital to increase profitability and save money in the maritime industry.
Freight prices are at their highest values in history.
Container freight rates are breaking all-time records. World Container Index experienced a 480% increase by reaching $8,795.77 for each 40 ft container between January 2020 and August 2021 (Drewry, 2021). The reasons behind this increase can be listed as that the mobility which started with the pandemic period together with other factors such as maritime trade wars, previously established and strengthened joint service structures, alternative routes, empty container problems, oil price volatility, the ship that blocked the Suez Canal, the spread of vaccine and normalization, increasing demands, supply shortages, Christmas preparation in global trade, and expected rapid growth in world trade. This shows that a new era has begun in maritime trade in the light of recent developments. A large container ship called Ever Given, owned by the Evergreen company, disturbed the sea traffic for 6 days in March 2021, when it went aground during its passage through the Suez Canal, which is the passage for 12% of world trade ( Figure 1). This incident caused commercial delays and financial losses in supply chains around the world. It is estimated that there is a loss of an average of 50 billion dollars.
With such an extreme breaking point that is due to a ship blocked a canal for 6 days, the dimensions of the dangers facing the maritime industry can be seen quite clearly when compared to the global epidemic (pandemic) that lasted for months.
Besides this, world trade is struggling with the empty container problem. Thus, many traders are facing challenges to deliver their export products to customers (Ship Technology, 2021).

Christmas preparations in global trade started early this
year. Global buyers, who were unable to fill their shelves before Christmas due to the supply disruptions last year because of the pandemic, are in a rush to restock by moving their orders to an earlier time to avoid a similar situation. Experts warn about the acceleration of trade may cause a new crisis in the container market, and besides the equipment shortage, freight prices, which have increased by 300% in the last year and a half, may have an increasing trend (Dunya, 2021).
Forecasting is an important tool for maintaining the competitiveness of container lines and ports, formulating appropriate short-medium term strategies, and planning. In Forecasting is one of the most significant elements for all types of industries and the maritime industry is not an exception. Since it is impossible to predict the events that affect the shipping market and they happen suddenly, the changes in the market are also fluctuating and stochastic (Goulielmos et al., 2009). However, such cycles and tendencies are not a new concept in the shipping industry. In fact, these are the integrated part of the industry for centuries (Stopford, 2009). Therewithal, being able to predict some of these swings can easily help carriers and shippers to capitalize on the fluctuations by allowing them to make the right decisions at the right times (Dixon, 2010).
In literature, several forecasting studies use maritime trade indices and volumes. The first study on time series is conducted by Klein & Verbeke (1987) and is the study carried out for the Antwerp port by using univariate time series with monthly data in Antwerp port. A multivariate time series model was used in another study for steel traffic flow in the Antwerp port (Klein & Verbeke, 1987). A long-term predictive value interval model was developed for forecasting the SCFI by fuzzy time series (Chou, 2017). Munim & Schramm (2017)

Materials and Methods
In the study, Shanghai Containerized Freight Index data from February 2016 to July 2021 was used. These data are modeled with the Python programming language. The proposed SCFI index forecasting methodology includes the following stages: describing the data and model, model identification and estimation, evaluation and forecasting, results.

Data and Model Description
Time series are well-defined data sets collected at variable time intervals and at equal time intervals. Analysis of time series includes some stages. Firstly, the data to be modeled should have a normal distribution. If the data is not normally distributed, the data will need to be converted to ensure the normal distribution of data. The conversion of data (such as square root or logarithms) ensures the fixation of the variance in a series with varying variation (Dasyam et al., 2015).
Later on, whether the series is stationary or not. Box-Jenkins model assumes that the time series is stationary. A stationary time series has a stationary mean, stationary variance, and stationary autocorrelation. These values are determined by using autocorrelation (ACF) and partial autocorrelation functions (PACF) and Dickey-Fuller (ADF) test (Awal & Siddique, 2011). Correlograms (ACF and PACF graphs) can show a stationarity pattern or a unit root with significant lags.
A more subjective way to evaluate is using (augmented) Dickey-Fuller (ADF) test statistics (Dickey & Fuller, 1979). The null hypothesis is that the series has a unit root. The alternative hypothesis is that the time series is stationary (or trendstationary).

Model Identification and Estimation
In the study, smoothing methods and the Box-Jenkins method were used in time series analysis.
A simple moving average (SMA) is an arithmetic moving average calculated by adding recent prices and then dividing that figure by the number of time periods in the calculation average. SMA is given as follows: With ( + ) observations of + , ℎ denotes a positive integer, is the seasonal indices, is the time period (Khogali et al., 2002).
Exponentially Weighted Moving Average (EWMA) will allow us to reduce the lag effect from SMA and EWMA will put more weight on values that occurred more recently. EWMA formula is as follows: where is the weight and is the time period of the series.
EWMA is a recursive process that continues until reaches the 0 (Lucas & Saccucci, 1990). The Holt-Winters method is a very common time series forecasting procedure capable of including both trend and seasonality. The method is also called "double exponential smoothing". Holt-Winter is used for exponential smoothing to make short-term forecasts by using "additive" or The component form for the multiplicative model is as follows: where is the integer part of (ℎ − 1)/ , which ensures ( ) stands for seasonal moving average polynomial as 1 , , … , acts as seasonal mobbing average parameter; ∇ signifies the seasonal difference which goes through the order (Yang et al., 2017).

Evaluation and Forecasting
In order to evaluate the forecasting model, Akaike information criterion (AIC): Bayesian information criterion (BIC): where is the number of estimated parameters, is the time period of the series, and is the maximum value of likelihood functions (Burnham & Anderson, 2004).

Results and Discussion
In the period from February 2016 to August 2021, SCFI is shown in Figure 2.    We can also address different types of change (growth/decay) in the trend. Our time series displays an exponential (curved) trend. We use a multiplicative adjustment. In Figure 4, we can see that Trible Exponential Smoothing is a much better representation of the time-series data. Although minor, it does appear that a multiplicative adjustment gives better results. Note that the green line almost completely overlaps the original data. RMSE and MAPE values were given in Table 1. In finding the performances of the resulting models, performance evaluation formulas provided in equations (1) and (2) were used. Also, forecast values for the August 2021-March 2022 periods are provided in Table 2. H0: Data has unit root and is non-stationary; H1: Data has no unit root and is stationary The Augmented Dickey-Fuller (ADF) test is applied for testing the stationarity for the data series presented in Table 3.   The ACF and PACF plots helps us to confirm stationarity.
The data are clearly non-stationary, with some seasonality, so we will first take a seasonal difference. The seasonally differenced data are shown in Table 3 Table 5, SARIMA (0,2,3) (1,0,0)12 is the found the most suitable model for forecasting SCFI.
Since model performance and diagnostics are controlled, the forecasting results can be examined 6-month forecasting is utilized with the SARIMA models. The forecasted values are also shown in Table 6. forecasting results are showed that the increase will continue ( Figure 8). Containerized Freight Index (SCFI) rose above 4,000 points for the first time in history. This increase can be associated with goods that are unable to be transported due to pandemic (lockdown), the intensive transportation of the goods that are kept in stock, and the increasing demands before Christmas, blocking off the Suez Channel by Evergreen, which happened suddenly during the transportation process that started after the pandemic, short-term breaks in world supply chains, empty container problem due to above-mentioned facts and the pandemic, and rises in inflation in the world. As a result of these developments, it is seen that the limited ship capacity leads to an increase in the freights in this current situation where transportation costs are increasing. Shipping market analysts can benefit from the performance of the proposed satisfactory forecasting models and integrate them into their administrative toolkits.