A strategic approach to forecasting shipping freight earnings.

Different strategic shipping decisions such as operations management, choice of charter contract and type of investment should be matched with the appropriate level and technique for freight earnings forecasting in order to achieve a closer outlook to future market conditions. A case study based on the tanker market.

Research motivation

In the long run, the shipping freight markets are considered one entity with common market sentiment, resulting in a highly correlated market with a hierarchical aggregation structure. However, in the short run, shipping freight markets are highly volatile, where the dynamics of freight revenues differ across various segments, depending on the market sector, the size of the vessel, and the underlying trading route at which each vessel operates, posing a significant challenge for forecasting shipping earnings in the short and long term.

This unique and complicated structure suggests that a mixed and flexible approach to forecasting is needed. However, the approach that the market is commonly using is to model and forecast the series either by considering each of the time series in isolation or by examining its interactions with other variables at the same level of the hierarchy, regardless of the strategic decision needed (i.e. operational, type of trade, investment).

This means that in terms of modelling and forecasting freight rates, the current practice focuses on a specific market level, thus ignoring the influence of the structure and hierarchy on freight rates. To better reflect the nature of the shipping markets, this study argues that to forecast freight indicators, market participants should generate forecasts across all possible freight routes at which each vessel operates, but also across each vessel type and even market segment to decide how to deploy their fleet but also how to invest their capital. This approach is known as hierarchical forecasting.

The main argument of this study is that strategic decision making for shipping practitioners should be based on forecasts of freight earnings at different hierarchical levels that better match the type of decision needed. In other words, different strategic shipping decisions such as operations management, choice of charter contract and type of investment should be matched with the appropriate level of forecasts of freight earnings that are aggregated at different macro-levels: operating route, vessel size and type of trade, and for different forecasting horizons: short-, medium- and long-run. This argument is presented graphically in Table 1.

Table 1: Hierarchical shipping decision matrix

Why hierarchy forecasting?

Shipping practitioners (shipowners, charterers, brokers, investors, etc.) face challenging strategic decisions that require valuing and assessing shipping revenues at different levels. Typically, such decisions are captured by the lower level of a hierarchical structure. On the one hand, decisions at the micro-operational level refer mainly to the choice of trading routes, type of contract to use (i.e. period time charter contract or spot voyage contract), bunker arrangements and steaming speeds. On the other hand, decisions at the macro-investment level refer to which segment and sector of the market to operate and are typically more macro-based.

A hierarchical time series can be disaggregated into subcategories that represent the structure of the whole entity. For example, total shipping earnings (or sales, fixtures, etc.) for the tanker (or drybulk, etc.) can be disaggregated by type of trade, such as dirty and clean. Each can be disaggregated further into subcategories reflecting the size of trade and the shipping route. The idea is to produce disaggregated forecasts based on disaggregated shipping time series, as we expect that forecast of lower-level shipping data adds up to give a forecast of subsequent higher levels, in the same way as the original data.


This research shows how the reconciliation of revenue forecasts produced at different levels can improve forecast accuracy and hence decision making in the shipping transportation sector. This may benefit shipping practitioners in making more informed decisions as a direct result of reconciled forecasts that consider the information at various levels of the hierarchy. This is important since the various components of the hierarchy can interact in varying and complex ways. A change in one series at one level can consequently impact other series at the same level and higher and lower levels. By modelling the entire hierarchy of a time series simultaneously, we can obtain better forecasts of the component series simply because such complex interactions can be accounted for.

By distinguishing between forecasts of freight earnings generated at different levels of the hierarchy, we present a model-independent framework that lies one conceptual level higher than the econometric models used for forecasting. The proposed methodology provides a link between strategic decision making in shipping and the hierarchical structure of freight earnings and matches the appropriate type of strategic decision with their corresponding forecasts aggregated at the appropriate level.

The results indicate that utilizing the proposed hierarchy structure can significantly improve long-term forecasting performance for shipping indicators.


Most empirical shipping research investigating freight dynamics using spot, Forward Freight Agreements (FFAs) and Time-Charter time series model freight rates across the same level of hierarchy and do not consider different levels of hierarchy. In practical terms, most proposed forecasting techniques and models produce good short-term forecasts (1-3 months) but fail to produce acceptable long-term forecasts.

The consensus from shipping empirical research is that univariate models are valuable tools for forecasting individual freight rate series. Therefore, this study produces forecasts at all levels using the most appropriate AutoRegressive Integrated Moving Average (ARIMA) model for each time series individually. Different optimal models (and coefficients) are estimated for each time series as we roll through the sample. Table 2 shows the percentage of times an order (autoregressive or moving average, seasonal or not) is selected as optimal at the various aggregation levels. We can see that, while the aggregated series appears to be white noise at the very top level, different models are identified as optimal at lower aggregation levels. Also, it should be noted that seasonality might exist at Size and Route levels, which is not the case for Trade or Total levels.

Table 2: Frequencies that each autoregressive and moving average order is identified as optimal in the fitted ARIMA model.

Hierarchical time series are commonly analyzed using either a “Top-Down” or a “Bottom-Up” method or a combination of the two. The top-down method entails forecasting the completely aggregated series and disaggregating the forecasts based on historical proportions. The bottom-up method involves forecasting each of the disaggregated series at the lowest level of the hierarchy and then using simple aggregation to obtain forecasts at higher levels of the hierarchy. In practice, many businesses combine these methods in what is sometimes called the “Middle-Out” method, where forecasts are obtained for each series at an intermediate level of the hierarchy, and then aggregation is used to obtain forecasts at higher levels and disaggregation is used to obtain forecasts at lower levels. This study uses forecasts produced by the bottom-up (BU) approach for benchmarking and forecast evaluations.

In brief, we apply and compare the following hierarchical approaches:

-Bottom-up approach is where forecasts are calculated only on the most granular level, and forecasts of other levels are directly derived as appropriate sums of the bottom level forecasts. We denote this approach as BU.
-Middle-out, where forecasts are produced at a middle level. We denote this approach as MO.
-Top-down approach, where only the forecast for the total is produced and subsequently disaggregated to the lower levels. We consider both disaggregations via historical and forecasted proportions, denoted by TDHP and TDFP.
-Simple combination approaches, where the forecasts derived from BU and TD are combined using equal weights. We denote these as COM.
-Optimal combination approach is based on the scaled weights as shown above. We denote this approach as COMB Optimal.

We only report results for the BU, TDFH, TDHP, and COM approaches in the case study.

Case study

To show how hierarchical structures can improve earnings forecasting performance, we use the tanker industry as an example.

The proposed hierarchical structure reflects the strong degree of substitutability of cargoes across different routes and shipping freight revenues, and their forecasts are aggregated at four levels. First, the lower level of the hierarchy represents shipping routes; forecasts generated at this level are more relevant for short-term operational decisions, such as fleet repositioning. Second, the middle-level hierarchy represents the market segment (size of vessel), and forecasts generated at this level are more relevant for long- to medium-term operational and investment decisions, such as fleet diversification. The third hierarchy represents the type of trade (dirty or clean), and forecasts generated at this level are more relevant for macro-level planning. Finally, the top-level reflects aggregate tanker earnings. This article only focuses on using the hierarchical forecasting approach to improve forecasts generated at the lower level of the hierarchical structure. The different hierarchy levels for trade, size and route are presented in Fig. 1. The primary data used in this study for the lower level of the hierarchy are tanker earnings for dirty and clean tankers. The underlying data are monthly freight earnings, measured in US dollars per day, known as time-charter-equivalent (TCE) rates. The details of the routes are reported in Table 3.

Figure 1: A shipping hierarchy structure for tanker earnings forecasting.

Figure 1 depicts shipping earnings aggregated at different levels according to the type of the tanker trade (dirty or clean), market segment across the same sector (e.g. Very Large Crude Carriers (VLCC) versus Suezmax tanker) as well as in terms of geographical criteria according to the underlying trade routes (e.g. East-bound or West-bound VLCC routes from Middle-East Gulf). The details of the routes are reported in Table 3. It describes the tanker shipping routes used in this study and reports the most disaggregated level of the hierarchy depicted in Figure 1.

Table 3: A description of the shipping routes and the hierarchical structure at the bottom level.


The data cover January 2009 to December 2021 for the dirty and clean tanker earnings subhierarchy. The entire sample consists of 6552 monthly observations covering 42 tanker routes, which means that each time series (tanker route) consisted of 156 monthly observations. Forecasting performance is evaluated over the last three years of the sample available data from 01/2019 till 12/2021 in a rolling origin manner. First, the in-sample period consists of data up to December 2018 and monthly forecasts for the next year 01/2019 till 12/ 2019, are produced. Then, the in-sample increases by one month and forecasts are produced for 02/2019 till 1/2020. The procedure is repeated until the forecast origin is the end of 2020 (12/2020 is the last available observation in the in-sample), and monthly forecasts are produced for 2021. The out-of-sample period is from January 2021 to December 2022, which is used to evaluate the forecasting performance of the proposed strategy.


Forecasting results are illustrated and reported in figure 2, showing percentage improvements of the best hierarchical approaches over the bottom-up (BU) approach for Tankers Earnings and the performance improvements for different forecasting horizons (in months). For example, the COM approach outperforms the BU approach over the long term in forecasting tanker earnings by 36.2%, 74.6% and 38.8% for forecasting horizons 7-9, 10-12 and 1-12 months, respectively, while for short-term forecasting the COM approach underperforms the BU approach by 35.7% and 1% for forecasting horizons 1-3 and 4-6 months, respectively. The results indicate a need for different approaches for forecasting tanker earnings in the short and long term. While the BU approach outperforms all other proposed approaches in forecasting freight earnings in the short-term (1-3 months), it is clear that long-term forecasts generated at the lower level are poor and unrepresentative of the structure of the shipping industry. Most importantly, the TDFP approach is superior in forecasting shipping earnings in the medium and long-term (4-12 months).

Figure 2: Percentage improvement over the benchmark (BM) approach for tanker earnings.

Table 4: A comparison of the forecasting accuracy of each approach.

Table 4 reports the predictive accuracy of the various hierarchical approaches for tanker earnings. Each entry in these tables reports the percentage of cases where an approach presented in rows is significantly better than an approach presented in columns. For example, the combined (COM) approach significantly outperforms the BU in 38.73% of the cases, while the BU significantly outperforms the COM in just 5.07%. The TDFP is the top performing approach for forecasting tanker earnings. On average, it significantly outperforms other approached in almost 28.6% of the cases, while the opposite is true in less than 7%.
In the following articles we explore using practical illustrations on how this forecasting approach can be combined with mathematical algorithms to make strategic decisions related to shipping operations and investment.

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