Forecasting Ships Prices and Their Influence on Maritime Insurance Market Ghiorghe Bătrînca Constanta Maritime University, Constanta, Romania gbatrinca@imc.ro Ana-Maria Burcă Academy of Economic Studies, Bucharest, Romania burca.anamaria@yahoo.com Abstract The shipping industry has been growing rapidly from year to year and until not too long ago, shipping was both the greatest beneficiary and hammering pulse of globalization. But now the global economic and financial crisis has stifled the boom of this industry. Since the global economic and financial crisis began in 2009, the problems the shipping industry faces have multiplied, generating a high volatility of prices. With the global expansion of the maritime sector, marine insurance is on the forefront nowadays, more than ever before. As the marine insurance premiums vary according to the value of insured assets and their number, the marine insurance market can be examined through the forecast of ships price in the context of deteriorating economic conditions. Keywords: ships price, marine insurance, ARIMA models, forecasting. Introduction Shipping market has passed through one of its most interesting periods in history between 2003 and 2009. It all started with significant increase in demand for raw materials in China coupled with low level of investment in new ships as a consequence of low productivity during 1990 s. Market participants were surprised to see such a significant increase in freight rates and many of them considered that this freight levels will not be sustainable for longer term. Few of the owners realized that the imbalance between supply and demand is rapidly growing and they ordered new ships at significantly higher prices than those available in the prior to 2003. More and more owners decided to order ships and soon shipyards run out of capacity and during 2007 and early 2008 it was almost impossible to find available space for building new ships before 2012. As a consequence of high freight rates, limited capacity of shipyards and significant increase of steel plates price the prices for ships reached unexpected levels. Market continued on a positive note till second half of 2008 when it was obvious that crisis affecting the banking sector would have a significant impact on demand for shipping services and during six months ships value decreased by more than 50 percent. This was somehow coupled with fears that as from 2010 supply will overpass demand and a long period of low freight level would be expected. Increase of ship prices had also a significant impact on industries supporting maritime industry, like banking and insurance, increasing lenders and insurers exposure to loss of a single asset. This paper will present the use of autoregressive integrated moving average (ARIMA) models for forecasting ships prices and will discuss about ships prices influence on maritime insurance market.
Literature review The advent of the computer popularized the use of autoregressive integrated moving average (ARIMA) models in many areas of science. But often, the research was of an empirical nature, using benchmark models as a comparison. The list of examples of real applications of ARIMA models include: electricity load by Di Caprio, Genesio, Pozzi and Vicino (1983), automobile insurance by Cummins and Griepentrog (1985), federal funds rate by Hein and Spudeck (1988), macroeconomic data by Dhrymes and Peristiani (1988), department store sales by Geurts and Kelly (1986,1990), Pack (1990), demand for telephone services by Grambsch and Stahel (1990), total population by Pflaumer (1992), tourism demand by Du Preez and Witt (2003) and so on. The existing researches on the use of ARIMA models in shipping industry are scarce. Container trade is of vital importance to liner shipping, waterfront activities and container port development. As container trade drives over fifty per cent by value of Australia s seaborne trade, Amoako (2002) carried out an analysis that provides an overview of container trade at national level and its future trends. The author generated forecasts of future levels of container quantities by using two different methods: dynamic econometric modeling and multivariate autoregressive modeling. The research was conceived with data that exclude double handling, because figures that include double handling or trans-shipment may invalidate growth forecasts. According to the final results, the proportion of goods traded internationally in containers is expected to increase. Nevertheless, the ARIMA model is a good predictor in the short term. Khan et al. (2004) analyzed the application of the autoregressive moving average method and the artificial neural network methods for the prediction of ship motion. An algorithm capable of predicting the motion of a ship is required for the successful deployment of a ship system currently used on ships that operate in open sea environments. The authors show that the artificial neural network is superior to autoregressive moving average techniques and is able to predict the ship motion satisfactorily for up to 10 seconds. They also try to combine multiple time series prediction techniques in order to obtain better overall results than the ones generated by individual techniques. Dashan and Apaydin (2012) investigated the waste amount from ships in Istanbul. The authors succeeded to forecast the amount of different waste collected from transit ships for next two years based on the data recorded between September 2005 and January 2010 by applying ARMA forecasting model. According to their results, the collected amount of waste oil, bilge water, sludge and garbage will increase, while those for ballast and slop will decrease. Overall, the current data remain between the upper and the lower limit values of forecasting data. Data and methodology In this study, the ARIMA models were applied in order to capture and examine the dynamics of the ship prices. For the empirical study, the monthly data series of Capesize ships price in real value for the period September 2003 April 2013 were used. The Capesize ships price was chosen because during the analyzed period it has recorded the highest volatility. Data were collected from Baltic Exchange database and the ARIMA models were built with EViews 7. The ARIMA model is widely used in the field of forecasting and there are a large number of variations of the model proposed in various literatures over the years (Stoica et al.,1999).
The Box-Jenkin s (1976) ARIMA modelling procedure considers the time-dependent nature of data to produce efficient estimation of a statistical model which can be interpreted as having generated the sample data. ARIMA specifically models dependent variables as a function of itself lagged from previous periods, i.e. autoregression, and random errors lagged from previous periods, i.e. moving-average. The ARIMA model is a generalization of the autoregressive and the moving average models. The autoregressive (AR) model uses past values of the dependent variable to explain the current value whereas, the moving average (MA) model uses lagged values of the error term to explain the current value of the explanatory variable. The general ARIMA model is called an ARIMA(p,d,q), with p being the number of lags of the dependent variable (the AR terms), d being the number of differences required to take in order to make the series stationary, and q being the number of lagged terms of the error term (the MA terms). An ARIMA(p,d,q) (AutoRegressive Integrated Moving Average with orders p,d,q) model is a discrete time linear equations with noise, of the form: p q k d k 1 α k L ( 1 L) X t = 1 + β k L ε t k = 1 k = 1 Taking in consideration the fact that the time series consist of monthly data, the testing of seasonality becomes imperious. Figure 1 indicates that the seasonality phenomenon is not relevant for the time series considered. 160 SHIP_PRICE by Season 140 120 100 80 60 40 20 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Means by Season Figure 1. Seasonal graph of ships price Firstly, the ADF test (Augmented Dickey-Fuller) was applied in order to verify the stationarity of time series. A time series is said to be stationary if its mean, variance and its covariances remain constant over time. From an economic point of view, shocks to a stationary time series are temporary and, over time, the effects of the shocks will dissipate. The existence of a unit root was estimated for the original data and the absence of a unit root for the first-difference logarithmic data (Table 1). Usually, the econometric analysis is performed with logarithmic series because it facilitates the interpretation of regression coefficients. Therefore, the variables are integrated of order 1 and denoted by l(1).
Table 1. The ADF test for first-difference logarithmic data If the probability is lower than the significance level (1%, 5% and 10%), the null hypothesis is rejected. It can be observed that the first-difference logarithmic data is stationary. Box and Jenkins first introduced ARIMA models in 1976, the term deriving from AR autoregressive, I integrated and MA moving average. Box and Jenkins designed a three-stage method which can be applied in order to estimate and select an appropriate ARIMA model. In the identification stage, the form of the model has to be discovered, because any model may be given more than one different representations. Once the time series stationarity is achieved, the next step is to identify the p and q orders of the ARIMA model. Therefore, the time plot of the series autocorrelation function (ACF) and partial correlation function (PACF) will be visually examined, because they offer access to useful information concerning outliers, missing values and structural breaks in the data (Table 2). Table 2. Autocorrelation function and partial correlation function From the table above, it can be observed that there are two significant spikes on the time plot of the series autocorrelation function (ACF), and then all are zero, while there are also two significant spikes in the partial correlation function (PACF). This suggests that the models might have up to MA(2) and AR(2) specifications. Thus, the possible models are the ARIMA(1,1,1), ARIMA(1,1,2), ARIMA(2,1,1) or ARIMA(2,1,2) models. According to Box and Jenkins, a valid model should be stationary and invertible. Thus, the modulus of each AR coefficient has to be lower than 1, the sum of AR coefficients has to be lower than 1 and the modulus of each root has to be lower than 1. These requirements are fulfilled by all the models that were identified in the previous stage.
In the estimation stage, each of the possible models is estimated and various coefficients are analyzed. The estimated models are compared using the Akaike information criterion (AIC), the Schwartz Bayesian criterion (SBC) and Adjusted R-squared (Table 3). The model that minimizes AIC and SBC and has the highest Adjusted R-squared will be chosen. Table 3. Summary results of possible ARIMA models Model ARIMA(1,1,1) ARIMA(1,1,2) ARIMA(2,1,1) ARIMA(2,1,2) AIC -2.764238-2.748539-2.751415-2.796414 SBC -2.692233-2.652532-2.654870-2.675734 Adjusted R- squared 0.504857 0.501277 0.497129 0.523317 According to Table 3, in terms of AIC and SBC, contradictory results were obtained: AIC suggests the ARIMA(2,1,2) model, but SBC suggests the ARIMA(1,1,1) model. But the ARIMA(2,1,2) model has the highest Adjusted R-squared, suggesting that this model is probably the most appropriate one. Therefore, the ARIMA(2,1,2) model is estimated in Table 4 and its validity is tested in Table 5. It can be noted that the model is stationary and invertible. Furthermore, R-squared and Adjusted R-squared tests are higher than 50%. Table 4. Estimation of ARIMA(2,1,2) model
Table 5. ARIMA(2,1,2) structure The last stage requires the examination of the goodness of fit of the model. Therefore, the statistical significance of model s coefficients, autocorrelation of residuals, homoskedasticity and the absence of additional ARCH terms will be tested. As it can be observed from Table 4, all the coefficients are statistically significant (the probabilities are lower than the significance level of 5% and 10%). Regarding the quality of residuals, the best view to look at first is Actual, Fitted, Residual Graph (Figure 2). It can be noted that the fit is quite good and the fitted values nearly cover up the actual values. The estimated model fits better in the later part than in the earlier years due to the fact that the residuals become smaller in absolute value..2.0 -.2 -.4.2 -.6.0 -.2 -.4 -.6 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Residual Actual Fitted Figure 2. Actual, Fitted, Residual Graph According to the correlogram of residuals (Table 6), there is no serial correlation of error terms (the null hypothesis is accepted because the probabilities of Q-stat are higher than the significance level).
Table 6. Correlogram of residuals According to F-statistic and Obs*R-squared tests which are higher than the 10% significance level (Table 7), the null hypothesis of absence of serial correlation of squared errors is accepted. Thus, there are no additional ARCH terms and the presence of homoskedasticity is accepted. Table 7. Heteroskedasticity ARCH test Taking in consideration the results of the tests applied to the estimated model, it can be concluded that the ARIMA(2,1,2) model is appropriate. By using this model, the Capesize ships price will be forecasted for the period May 2013 December 2016. Figure 3 illustrates the dynamic forecast of Capesize ships price and its error margins.
140 120 100 80 60 40 20 0-20 II III IV I II III IV I II III IV I II III IV 2013 2014 2015 2016 SHIP_PRICEF2 ± 2 S.E. Figure 3. Dynamic forecast of Capesize ships price Figure 4 illustrates the fluctuation of Capesize ships price during September 2003 December 2016. 160 SHIP_PRICEF2 140 120 100 80 60 40 20 03 04 05 06 07 08 09 10 11 12 13 14 15 16 Figure 4.The evolution of Capesize ships price The end users of this study can be represented by the specialists in the maritime industry and in the industries supporting the maritime industry, namely insurance and banking, who are directly or indirectly affected and concerned about ships price fluctuation. Conclusions As it can be observed from Figure 3, the Capesize ships price will record a continuously slight increase during May 2013 December 2016. Today s ship prices for Capesize vessels are at their historic minimum and once the gap between supply and demand will be reduced, prices will start moving up. One other aspect that has to be taken into consideration when looking at this graph is related to the fact data used in this study refer to prices for 5 years old ships which had a very unusual movement during 2007 and 2008 when they were over 30% higher than prices for new buildings. While this can be easily explained by the fact that five years old ships were able to trade immediately in an extraordinary high
market, while new ships were expected to be delivered in at least 24 months when nobody could have predicted the market level. As the marine insurance premiums vary according to the value of insured assets and their number, their evolution during May 2013 December 2016 can be examined through the forecast of ships price. As the value of the ships will start increasing again, it can be expected the exposure to loss of a single ship to increase. The oversupply of ships will probably drive out of the market old ships and sometime substandard ships, which is expected to have a positive influence on the insurance market profitability. References Amoako, J. (2002) Forecasting Australia s International container trade, 25 th Australasian Transport Research Forum. Baltic Exchange website http://www.balticexchange.com/ Cummins, J. D. and Griepentrog, G. L. (1985) Forecasting automobile insurance paid claims using econometric and ARIMA models, International Journal of Forecasting, 1, 203 215. Dashan, E.S. and Apaydin, O. (2013) An Investigation On Waste Amount From Ships in Istanbul, Global NEST Journal, Volume 15, No 1, 49-56. De Gooijer, J. G. and Hyndman, R.J. (2006) 25 years of time series forecasting, International Journal of Forecasting, 22, 443 473. Dhrymes, P. J. and Peristiani, S. C. (1988) A comparison of the forecasting performance of WEFA and ARIMA time series methods, International Journal of Forecasting, 4, 81 101. Di Caprio, U., Genesio, R., Pozzi, S. and Vicino, A. (1983) Short term load forecasting in electric power systems: A comparison of ARMA models and extended Wiener filtering, Journal of Forecasting, 2, 59 76. Du Preez, J. and Witt, S. F. (2003) Univariate versus multivariate time series forecasting: An application to international tourism demand, International Journal of Forecasting, 19, 435 451. Geurts, M. D. and Kelly, J. P. (1986) Forecasting retail sales using alternative models, International Journal of Forecasting, 2, 261 272. Geurts, M. D. and Kelly, J. P. (1990) Comments on: In defense of ARIMA modeling by D.J. Pack, International Journal of Forecasting, 6, 497 499. Grambsch, P. and Stahel, W. A. (1990) Forecasting demand for special telephone services: A case study, International Journal of Forecasting, 6, 53 64. Hein, S. and Spudeck, R. E. (1988) Forecasting the daily federal funds rate, International Journal of Forecasting, 4, 581 591. Khan, A., Cees, B., Kaye, M. and Crozier, M. (2004) Real Time Prediction Of Ship Motions and Attitudes Using Advanced Prediction Techniques, 24th International Congress Of The Aeronautical Sciences.
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