Tsolakis et al. [25]

Error correction model; comparison with AR; test for co-integration (Johansen, (1991) [3] ) 5% level is >0. Neither autocorrelation or heteroskedasticity; OLS estimator is BLUE

Used ships prices; annual data; stationarity secured by 1st differences in all relationships by ADF

New ships prices and time charters affect used ship prices; cost of capital valid only for bulk carriers; mixed results among sizes; order-book causes used ships’ prices to fall in cases

Tvedt [54]

Dry bulk market

He challenged the 1st differences stationarity of most shipping time series; if data transformed by a conversion from $ to yen, series became stationary…

Adland et al. [55]

Valuation model; Co-integration; pricing the forward ship value agreements; GARCH

2nd hand ship market

Unbiasedness of implied forward prices in the 2nd hand ship market; market efficiency exists

Adland & Koekebakker [56]

A mathematical model to value forward time charter & spot rates

Option valuation; empirical volatility of forward freight rates; valuing ship prices. Brokers’ quotations

A model of forward freight rates

dynamics; time charter rates

Adland & Cullinane [57]


General non-parametric Markov diffusion model

Spot freight rates in tanker markets;

this is mean reverting… in the extremes; volatility of freight rate changes increase with its level

They challenged that the 1st differencing in a VAR model is necessary, if series are truly stationary