scholarly journals Autoregressive Modeling of Forest Dynamics

Forests ◽  
2019 ◽  
Vol 10 (12) ◽  
pp. 1074
Author(s):  
Olga Rumyantseva ◽  
Andrey Sarantsev ◽  
Nikolay Strigul
Keyword(s):  
Random Walk ◽  
Forest Dynamics ◽  
Forest Biomass ◽  
Autoregressive Process ◽  
Autoregressive Models ◽  
Forest Inventories ◽  
Continuous State Space ◽  
Continuous State ◽  
Yearly Average ◽  
Geometric Random Walk

In this work, we employ autoregressive models developed in financial engineering for modeling of forest dynamics. Autoregressive models have some theoretical advantage over currently employed forest modeling approaches such as Markov chains and individual-based models, as autoregressive models are both analytically tractable and operate with continuous state space. We performed a time series statistical analysis of forest biomass and basal areas recorded in Quebec provincial forest inventories from 1970 to 2007. The geometric random walk model adequately describes the yearly average dynamics. For individual patches, we fit an autoregressive process (AR) of order 1 capable to model negative feedback (mean-reversion). Overall, the best fit also turned out to be geometric random walk; however, the normality tests for residuals failed. In contrast, yearly means were adequately described by normal fluctuations, with annual growth on average of 2.3%, but with a standard deviation of order of 40%. We used a Bayesian analysis to account for the uneven number of observations per year. This work demonstrates that autoregressive models represent a valuable tool for the modeling of forest dynamics. In particular, they quantify the stochastic effects of environmental disturbances and develop predictive empirical models on short and intermediate temporal scales.

On coupling of random walks and renewal processes

1996 ◽  
Vol 33 (1) ◽  
pp. 122-126
Author(s):  
Torgny Lindvall ◽  
L. C. G. Rogers
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Simple Random Walk ◽  
Renewal Processes ◽  
Renewal Theorem ◽  
One Dimensional ◽  
Continuous State Space ◽  
Continuous State ◽  
Efficient Coupling ◽  
Blackwell's Renewal Theorem

The use of Mineka coupling is extended to a case with a continuous state space: an efficient coupling of random walks S and S' in can be made such that S' — S is virtually a one-dimensional simple random walk. This insight settles a zero-two law of ergodicity. One more proof of Blackwell's renewal theorem is also presented.

The extremal index for a Markov chain

1992 ◽  
Vol 29 (01) ◽  
pp. 37-45 ◽  
Author(s):  
Richard L. Smith
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Extreme Values ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Extremal Index ◽  
Scaling Properties ◽  
Continuous State Space ◽  
Continuous State ◽  
Tail Behaviour

The paper presents a method of computing the extremal index for a discrete-time stationary Markov chain in continuous state space. The method is based on the assumption that bivariate margins of the process are in the domain of attraction of a bivariate extreme value distribution. Scaling properties of bivariate extremes then lead to a random walk representation for the tail behaviour of the process, and hence to computation of the extremal index in terms of the fluctuation properties of that random walk. The result may then be used to determine the asymptotic distribution of extreme values from the Markov chain.

The extremal index for a Markov chain

1992 ◽  
Vol 29 (1) ◽  
pp. 37-45 ◽  
Author(s):  
Richard L. Smith
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Extreme Values ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Extremal Index ◽  
Scaling Properties ◽  
Continuous State Space ◽  
Continuous State ◽  
Tail Behaviour

The paper presents a method of computing the extremal index for a discrete-time stationary Markov chain in continuous state space. The method is based on the assumption that bivariate margins of the process are in the domain of attraction of a bivariate extreme value distribution. Scaling properties of bivariate extremes then lead to a random walk representation for the tail behaviour of the process, and hence to computation of the extremal index in terms of the fluctuation properties of that random walk. The result may then be used to determine the asymptotic distribution of extreme values from the Markov chain.

scholarly journals Time Series Analysis of Forest Dynamics at the Ecoregion Level

Forecasting ◽  
2020 ◽  
Vol 2 (3) ◽  
pp. 364-386
Author(s):  
Olga Rumyantseva ◽  
Andrey Sarantsev ◽  
Nikolay Strigul
Keyword(s):  
Time Series ◽  
Random Walk ◽  
Forest Inventory ◽  
Forest Dynamics ◽  
Heavy Tails ◽  
Basal Area ◽  
Forest Growth ◽  
Ecological Regions ◽  
Ecological Region ◽  
Geometric Random Walk

Forecasting of forest dynamics at a large scale is essential for land use management, global climate change and biogeochemistry modeling. We develop time series models of the forest dynamics in the conterminous United States based on forest inventory data collected by the US Forest Service over several decades. We fulfilled autoregressive analysis of the basal forest area at the level of US ecological regions. In each USA ecological region, we modeled basal area dynamics on individual forest inventory pots and performed analysis of its yearly averages. The last task involved Bayesian techniques to treat irregular data. In the absolute majority of ecological regions, basal area yearly averages behave as geometric random walk with normal increments. In California Coastal Province, geometric random walk with normal increments adequately describes dynamics of both basal area yearly averages and basal area on individual forest plots. Regarding all the rest of the USA’s ecological regions, basal areas on individual forest patches behave as random walks with heavy tails. The Bayesian approach allowed us to evaluate forest growth rate within each USA ecological region. We have also implemented time series ARIMA models for annual averages basal area in every USA ecological region. The developed models account for stochastic effects of environmental disturbances and allow one to forecast forest dynamics.

On coupling of random walks and renewal processes

1996 ◽  
Vol 33 (01) ◽  
pp. 122-126
Author(s):  
Torgny Lindvall ◽  
L. C. G. Rogers
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Simple Random Walk ◽  
Renewal Processes ◽  
Renewal Theorem ◽  
One Dimensional ◽  
Continuous State Space ◽  
Continuous State ◽  
Efficient Coupling ◽  
Blackwell's Renewal Theorem

The use of Mineka coupling is extended to a case with a continuous state space: an efficient coupling of random walks S and S' in can be made such that S' — S is virtually a one-dimensional simple random walk. This insight settles a zero-two law of ergodicity. One more proof of Blackwell's renewal theorem is also presented.

scholarly journals Reinforcement learning versus swarm intelligence for autonomous multi-HAPS coordination

2021 ◽  
Vol 3 (6) ◽  
Author(s):  
Ogbonnaya Anicho ◽  
Philip B. Charlesworth ◽  
Gurvinder S. Baicher ◽  
Atulya K. Nagar
Keyword(s):  
Reinforcement Learning ◽  
State Space ◽  
Swarm Intelligence ◽  
Performance Indicators ◽  
Convergence Rates ◽  
Tuning Parameters ◽  
Continuous State Space ◽  
Continuous State ◽  
User Coverage ◽  
Better Than

AbstractThis work analyses the performance of Reinforcement Learning (RL) versus Swarm Intelligence (SI) for coordinating multiple unmanned High Altitude Platform Stations (HAPS) for communications area coverage. It builds upon previous work which looked at various elements of both algorithms. The main aim of this paper is to address the continuous state-space challenge within this work by using partitioning to manage the high dimensionality problem. This enabled comparing the performance of the classical cases of both RL and SI establishing a baseline for future comparisons of improved versions. From previous work, SI was observed to perform better across various key performance indicators. However, after tuning parameters and empirically choosing suitable partitioning ratio for the RL state space, it was observed that the SI algorithm still maintained superior coordination capability by achieving higher mean overall user coverage (about 20% better than the RL algorithm), in addition to faster convergence rates. Though the RL technique showed better average peak user coverage, the unpredictable coverage dip was a key weakness, making SI a more suitable algorithm within the context of this work.

scholarly journals Instantaneous brain dynamics mapped to a continuous state space

NeuroImage ◽  
2017 ◽  
Vol 162 ◽  
pp. 344-352 ◽  
Author(s):  
Jacob C.W. Billings ◽  
Alessio Medda ◽  
Sadia Shakil ◽  
Xiaohong Shen ◽  
Amrit Kashyap ◽  
...  
Keyword(s):  
State Space ◽  
Brain Dynamics ◽  
Continuous State Space ◽  
Continuous State

On Asymptotic Prediction Problems for Multivariate Autoregressive Models in the Unstable Nonexplosive Case

1987 ◽  
Vol 36 (1-2) ◽  
pp. 29-38 ◽  
Author(s):  
A. K. Basu ◽  
S. Sen Roy
Keyword(s):  
Autoregressive Process ◽  
Autoregressive Models ◽  
Multivariate Autoregressive Models ◽  
Prediction Problems ◽  
Dependent Error ◽  
Meansquare Error ◽  
Multivariate Autoregressive

This paper considers the prediction problems of a k-dimensional, pth order autoregressive process with unstable but non-explosive roots and dependent error variables. The estimated predictor has been shown to be asymptotically equivalent to the optimal predictor. An expression for the meansquare error of the estimated predictor has also been derived .

Temporal aggregation of random walk processes and implications for economic analysis

2019 ◽  
Vol 24 (2) ◽  
Author(s):  
Yamin S Ahmad ◽  
Ivan Paya
Keyword(s):  
Random Walk ◽  
Autoregressive Process ◽  
Potential Effect ◽  
Temporal Aggregation ◽  
Time Averaging ◽  
Fat Tails ◽  
Data Generating Process ◽  
Variance Ratios ◽  
Interval Sampling ◽  
The Impact

AbstractThis paper examines the impact of time averaging and interval sampling data assuming that the data generating process for a given series follows a random walk with iid errors. We provide exact expressions for the corresponding variances, and covariances, for both levels and higher order differences of the aggregated series, as well as that for the variance ratio, demonstrating exactly how the degree of temporal aggregation impacts these properties. We empirically investigate this issue on exchange rates and find that the values of the variance ratios and autocorrelation coefficients at different frequencies are consistent with our theoretical results. We also conduct a simulation exercise that illustrates the potential effect that conditional heteroskedasticity and fat tails may have on the temporal aggregation of a random walk and of a highly persistent autoregressive process.

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