Week 6: Applied Time-Series Analysis for Fisheries and Environmental Data

Class material: webpage

Week 6: Introduction to including covariates in multivariate time-series model
This week we introduce the inclusion of covariates using the framework of a multivariate autoregressive model written in state-space form.  You will understand the lecture better if you read the chapter on covariates in the MARSS User Guide first.  Much of the lecture is about how to include covariates in different mathematically equivalent ways.  You'll want to translate the R code in the lecture into the mathematical formulas (matrix form) to see how covariates are entering the mathematical model.


Lab topic:
The main lab is to go through the covariate chapter and examples in the MARSS User Guide.  Then we have some salmon data to play with to try different ways of including cycles (in this case driven by cohort strength) into an analysis.

Lecture 6
Click the big arrow to start.  You can also find the ppt of lecture t on the class webpage.

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Week 5: Applied Time-Series Analysis for Fisheries and Environmental Data

Class material: webpage

Week 5: Introduction to multivariate autoregressive state-space models
Lecture topics:

• Review of dealing with obs error with ARIMA (from last week)
• Multivariate state space models
• How these are expressed mathematically
• Analysis of multi-site data using this framework
• Parameter estimation: Kalman filter, Newton methods and EM algorithm

Lab topic:
The main lab is to go through case study 2 in the MARSS User Guide. I have a Fish 507 specific version of the case study code on the course website with questions to answer as you go through. Case study 3 and 8 are optional but going through them will help solidify your understanding of multivariate state-space models. Do go through the ARMA code as it discusses some important points about the effects of data transformation (in this case differences) on the time-series model that is appropriate for the data.

Lecture 5
Click the big arrow to start the show. You can also find just a pdf of lecture 5 on the class webpage.

Week 4: Applied Time-Series Analysis for Fisheries and Environmental Data

Class material: webpage

Week 4: Introduction to univariate autoregressive state-space models
Topics:

• State-space models
• Process versus observation error
• Model Selection

Lecture 4
Click the big arrow to start the show. You can also find just the ppt of lecture 3 on the class webpage.

Week 3: Applied Time-Series Analysis for Fisheries and Environmental Data

Class material: webpage

Week 3: Estimation, model selection, and forecasting for time series models
Topics:

• Summarizing ARIMA models
• Estimation
• Model Selection
• Prediction & forecasting
• Evaluating forecasts
• Functions: arima(), lm(), Arima()

Lecture 3
This is our second attempt at recording a lecture. Still much to be learned but we are getting better.  Click the big arrow to start the show. You can also find just the ppt of lecture 3 on the class webpage.

Week 2: Applied Time-Series Analysis for Fisheries and Environmental Data

Class material: webpage

Week 2: Correlation, stationarity & stationary time-series models
The lecture introduces the ACF, PACF, and basic properties of AR, MA and ARMA models. The computer code section shows R code to analyze simulated time-series data so that participants get a feel for ACF and PACF and get a feel for AR and MA processes. The participants then move to analyzing some real time-series data using the 30+ year time-series of Lake Washington plankton.

Lecture 2
This is our first attempt at recording a lecture. Ahem, there is clearly much to be learned to improve the process...Click the big arrow to start the show. You can also find just the ppt of lecture 2 on the class webpage.

Winter stats reading group starting up: Hierarchical Modeling and Analysis for Spatial Data

The NWFSC/SAFS stats reading group is reading "Hierarchical Modeling and Analysis for Spatial Data" by Banerjee et al. this quarter.  Fridays 3pm at SAFS 229 during Winter Qtr 2013.  Open to interested statistical ecologists.  Contact Eli.

New paper on spatial-temporal time series modeling

New paper just out by Eric Ward using Bayesian state-space time-series models.

"Applying time series models with spatial correlation to identify the scale of variation in habitat metrics related to threatened coho salmon (Oncorhynchus kisutch) in the Pacific Northwest"
Eric J. Ward, George R. Pess, Kara Anlauf-Dunn, and Chris E. Jordan
Canadian Journal of Fisheries and Aquatic Science (link to paper)

Abstract: Trend analyses are common in the analysis of fisheries data, yet the majority of them ignore either observation error or spatial correlation. In this analysis, we applied a novel hierarchical Bayesian state-space time series model with spatial correlation to a 12-year data set of habitat variables related to coho salmon (Oncorhynchus kisutch) in coastal Oregon, USA. This model allowed us to estimate the degree of spatial correlation separately for each habitat variable and the importance of observation error relative to environmental stochasticity. This framework allows us to identify variables that would benefit from additional sampling and variables where sampling could be reduced. Of the eight variables included in our analysis, we found three metrics related to habitat quality correlated at large spatial scales (gradient, fine sediment, shade cover). Variables with higher observation error (pools, active channel width, fine sediment) could be made more precise with more repeat visits. Our spatio-temporal model is flexible and extendable to virtually any spatially explicit monitoring data set, even with large amounts of missing data and no repeated observations. Potential extensions include fisheries catch data, abiotic indicators, invasive species, or species of conservation concern.