Is spurious behaviour an issue for two independent stationary spatial autoregressive SAR(1) processes?
Spurious regression occurs when two independent stationary or nonstationary time series are found to be correlated. Spurious behaviour is also detected in spatial data. Using a Monte Carlo analysis, this study examines the spurious phenomenon for two independent stationary spatial autoregressive processes of order one, that is, SAR(1), and it finds that when spatial econometric models are estimated, as suggested by the LM specification tests, the spurious behaviour is not detected nor the presence of spatially autocorrelated errors.
Unit Roots and Deterministic Trends in Spatial Econometric Models
This article reflects on the relevance of the concept of unit roots in the spatial context. The initial introduction of this topic in the time-series literature caused significant changes in the mainstream econometric methodology. However, the literature specialized in spatial econometric modeling has not extensively dealt with this issue. The current article continues the discussion of the concept of unit roots employed in a spatial context and presents a series of peculiarities that should be noticed. Subsequently, attention focuses on the topic of deterministic trends associated with the scale factor that intervenes in autoregressive spatial processes. The incidence of this type of trend should not be neglected. It induces the risk of finding spurious correlation that should be taken into account.
Lake Muzahi, Rwanda: limnological features and phytoplankton production
Lake Muhazi, a small lake of Rwanda (East Africa) was studied from 1986 to 1990. A dramatic decrease of the catch of Oreochromis niloticus (350 T y−1 in the fifties vs 30 T y−1 in 1982) suggested a loss of productivity or overfishing. In the same period, other ecological changes occurred: the submerged macrophytes regressed and there was a decrease in Secchi depth (0.65 m in 1987 vs 1.5 m in the fifties). Compared to other lakes of the same area, the plankton production seemed low. The results of the present study characterize lake Muhazi as a shallow lake with a rather unstable diurnal stratification and with slight differences in mixing regime between its eastern, deepest part and its western, shallowest part. Secchi disk depth does not vary seasonally to a large extent. The water has a rather high mineral content (conductivity of about 500 µS cm−1 at 25 °C) and low concentrations of dissolved N and P, except in the hypolimnion, where NHinf4sup+-N can be high.Two species, Microcystis aeruginosa and Ceratium hirundinella, account for most of the phytoplankton biomass, which is about 50–80 mg chlorophyll a m−2 in the euphotic zone, usually with little seasonal variation. Daily gross production estimates amount to about 6 to 9.5 g O2 m−2 d−1 with a significant difference between the two parts of the lake. Data on C:N and C:P ratio in the phytoplankton suggest that some N deficiency might occur in the eastern part. Moreover, the Zm:Zc ratio could also lead to rather low net production rates (0.21–0.25 d−1 for a mixed layer of 4 m)In conclusion, the primary production of lake Muhazi is medium for African lakes and the hypothesis that decreased planktonic production could account for a reduced fish production should be discarded. Whereas the present yield of the fishery is only 20 kg ha−1 y−1, the yield estimated from primary production ranges between 46 and 64 kg ha−1 y−1. This could be reached through proper management. Finally, some hypotheses are given to explain the ecological changes which occurred in the lake.