Texts
A classic time-series econometrics text is Hamilton (1994), Time Series Analysis, Princeton University Press.
A fine and modern text (with useful R code) from a purely statistical perspective is Shumway and Stoffer (2011, third edition), Time Series Analysis and its Applications, with R Examples, Springer.
A new time-series econometrics text is Martin, Hurn and Harris (2012), Econometric Modelling with Time Series: Specification, Estimation and Testing, Cambridge University Press, in press. It is available on the course Blackboard site.
Here is some background reading, complementing rather than substituting for lectures:
Introduction to R: Shumway and Stoffer appendix R
Review of Asymptotic Theory in Dynamic Environments: Hamilton chs. 7-8; Shumway and Stoffer appendix A; Martin et al. chs. 1-2
Linear Time Series in the Time Domain: Hamilton chs. 1-4, 10-11; Shumway and Stoffer chs. 1-3, appendix B; Martin et al. chs. 13-15
Linear Time Series in the Frequency Domain: Hamilton ch. 6; Shumway and Stoffer ch. 4, appendix C
Elements of Markovian Structure: Hamilton, ch. 22
State-Space and the Kalman Filter: Hamilton ch. 13; Shumway and Stoffer ch. 6; Martin et al. ch. 15
Interesting Models (in State Space): Hamilton ch. 13; Shumway and Stoffer ch. 6; Martin et al. ch. 15
Simulation and Simulation-Based Methods: Davidson and McKinnon, ch. 21; Shumway and Stoffer ch. 6
Gaussian MLE in Time and Frequency Domains (Including Numerical Optimization): Hamilton chs. 5, 13; Shumway and Stoffer chs. 3, 6, 7; Martin et al. chs. 1, 2, 9, 15 (Numerical Optimization: Hamilton ch. 5; Shumway and Stoffer ch. 6; Martin et al. ch. 3)
Bayesian Analysis and Filtering: Hamilton ch. 12, Shumway and Stoffer ch. 6; Koop; Kim and Nelson
Integration, Cointegration and Long Memory: Hamilton chs. 15-20; Shumway and Stoffer chs. 3, 5; Martin et al. chs. 16-18
Nonlinear / Non-Gaussian State Space: Hamilton ch. 22; Shumway and Stoffer ch. 6
Volatility: Hamilton ch. 21; Shumway and Stoffer ch. 5; Martin et al. ch. 20
Useful Additional Books Worth Encountering
Beran, J. (1994), Statistics for Long-Memory Processes. New York: Chapman and Hall.
Box, G.E.P. and Jenkins, G.W. (1970 and later eds.), Time Series Analysis, Forecasting and Control. Englewood Cliffs, New Jersey: Prentice-Hall.
Davidson, R. and MacKinnon, J. (1993), Estimation and Inference in Econometrics. Oxford: Oxford University Press.
Diebold, F.X. (2007), Elements of Forecasting (fourth edition). Cincinnati: South-Western.
Durbin, J. and Koopman, S.J. (2001), Time Series Analysis by State Space Models. Oxford: Oxford University Press.
Efron, B. and Tibshirani, R.J. (1993), An Introduction to the Bootstrap. New York: Chapman and Hall.
Elliott, G., Granger, C.W.J. and Timmermann, A., eds. (2005), Handbook of Economic Forecasting. Amsterdam: North-Holland.
Engle, R.F. and McFadden, D., eds. (1995), Handbook of Econometrics, Volume 4. Amsterdam: North-Holland.
Geweke, J. Koop, G. and van Dijk, H., eds. (2011), The Oxford Handbook of Bayesian Econometrics. Oxford University Press.
Granger, C.W.J. and Newbold, P. (1977 and later eds.), Forecasting Economic Time Series. Orlando, Florida: Academic Press.
Granger, C.W.J. and Teräsvirta, Y. (1996), Modeling Nonlinear Economic Relationships. Oxford: Oxford University Press.
Hall, P. (1992), The Bootstrap and Edgeworth Expansion. New York: Springer Verlag.
Hammersley, J.M. and Handscomb, D.C. (1964), Monte Carlo Methods. London: Chapman and Hall.
Hansen, L.P. and Ait-Sahalia, A., eds. (2010), Handbook of Financial Econometrics. Amsterdam: North-Holland.
Harvey, A.C. (1989), Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge: Cambridge University Press.
Harvey, A.C. (1993 and later eds.), Time Series Models. Cambridge: MIT Press.
Hastie, T., Tibshirani, R. and Friedman, J. (2001), The Elements of Statistical Learning: Data Mining, Inference and Prediction. New York: Springer-Verlag.
Kim, C.-J. and Nelson, C.R. (1999), State-Space Models with Regime Switching. Cambridge: MIT Press.
Koop, G. (2004), Bayesian Econometrics. John Wiley.
Nerlove, M., Grether, D.M., Carvalho, J.L. (1979 and later eds.), Analysis of Economic Time Series: A Synthesis. New York: Academic Press.
Priestley, M. (1981), Spectral analysis and Time Series. New York: Academic Press.
Shephard, N., ed. (2005), Stochastic Volatility: Selected Readings. Oxford: Oxford University Press.
Silverman, B.W. (1986), Density Estimation for Statistics and Data Analysis. New York: Chapman and Hall.
Whittle, P. (1963 and later eds.), Prediction and Regulation by Linear Least Squares Methods. Minneapolis: University of Minnesota Press.
Zellner, A. (1971), An Introduction to Bayesian Inference in Econometrics. New York: John Wiley and Sons.