¹ For an example of the latter, with a brief review of the existing literature, see Brown, P. and Payne, C., ‘Election Night Forecasting’, Journal of the Royal Statistical Society, Series A, 138 (1975), 463–98CrossRefGoogle Scholar. For an example of prediction not restricted to election nights see Budge, I. and Farlie, D., Voting and Party Competition (London and New York: Wiley, 1977), Chap. 12 passim.Google Scholar

² For a review of this field see Frey, B. S. and Schneider, F., ‘On the Modelling of Politico-economic Interdependence’, European Journal of Political Research, III (1975), 339–60CrossRefGoogle Scholar. For Britain see Goodhart, C. and Bhansali, R., ‘Political Economy’, Political Studies, XVIII (1970), 43–106CrossRefGoogle Scholar and Miller, W. and Mackie, M., ‘The Electoral Cycle and the Asymmetry of Government and Opposition Popularity: An Alternative Model of the Relationship between Economic Conditions and Political Popularity’, Political Studies, XXI (1973), 263–79CrossRefGoogle Scholar. For the United States see Mueller, J. E., ‘Presidential Popularity from Truman to Johnson’, American Political Science Review, LXIV (1970), 18–34CrossRefGoogle Scholar; and Stimson, J. A., ‘Public Support for American Presidents: A Cyclical Model’, Public Opinion Quarterly, XL (1976), 1–11CrossRefGoogle Scholar. For the Federal Republic of Germany see Kirchgässner, C., ‘Okonometrische Untersuchungen des Einflusses der Wirtschaftslage auf die Popularität der Partien’, Schweizerische Zeitschrift für Volkswirtschaft und Statistik, CX (1974), 409–45.Google Scholar

³ See Box, G. and Jenkins, G., Time Series Analysis: Forecasting and Control (San Francisco: Holden Day, 1970)Google Scholar. For a summary of their work see Box, G. and Jenkins, G., ‘Some Recent Advances in Forecasting and Control’, Journal of the Royal Statistical Society, Series C, 17 (1968), 92–109.Google Scholar

⁴ For example, in the case of a first-order autoregressive process

where r ₁ and r ₂ are the autocorrelation coefficients between observations up to t and observations up to t−1 and t−2 respectively. ø₁₂ is the partial autocorrelation coefficient. See Box, G. and Jenkins, G., ‘Time Series Analysis’, pp. 64–5.Google Scholar

⁵ From (7) it can be seen that

We seek to find values of ø and θ which minimize But to obtain a ₁ it is necessary to know a _t−1, which is not available. Thus the procedure involves assigning starting values to a _t−1 (usually zero), and then calculating the sum of squared residuals. The lagged value of the residuals can then be used in a subsequent estimation to obtain a better fit. The procedure is repeated iteratively until the parameter values converge on stable values. For a full discussion of this see Anderson, O. N., Time Series Analysis and Forecasting: The Box-Jenkins Approach (London and Boston: Butterworths, 1976), Chap. 8.Google Scholar

⁶ The one application of Box-Jenkins modelling to political science is by Hibbs. Using British unemployment data for the period 1948–75 he assessed the effects of Government policy interventions on the level of unemployment. See Hibbs, D. A., ‘On Analyzing the Effects of Policy Interventions: Box-Jenkins and Box-Tiao versus Structural Equation Models’ in Heise, D., ed., Sociological Methodology (San Francisco and Washington: Jossey-Bass, 1977), pp. 137–79Google Scholar. See also Hibbs, D. A., ‘Political Parties and Macroeconomic Policy’, American Political Science Review, LXXI (1977), 1467–87CrossRefGoogle Scholar, where he examines United States' unemployment data as well as the United Kingdom data.

⁷ Reid, D. J., ‘A Comparison of Forecasting Techniques on Economic Time Series’, in Bramson, M. J., ed., Forecasting in Action (London: Operational Research Society, 1972)Google Scholar. Reid used a set of 113 time series, consisting mainly of economic variables, and examined the comparative efficiency of different forecasting techniques.

⁸ The data were obtained from various issues of the Gallup Political Index (London: Gallup Poll Ltd.) except for some of the earlier post-war data which was kindly supplied by Mr C. A. Goodhart. The data for the parties represent the percentage of respondents who chose that particular party in response to the question: ‘If there were a General Election tomorrow, how would you vote?’ The series used was Series C in the Gallup Political Index, i.e. the observations with ‘don't knows’ excluded, since these provide a better fit for electoral forecasting. The data on ‘prime minister's popularity’ refers to the percentage of respondents satisfied with the job Mr X is doing as prime minister. ‘Government popularity’ refers to the percentage support for the incumbent party minus the percentage support for the opposition party, using the above question, and again excluding the ‘don't knows’.

⁹ See Box, and Jenkins, , ‘Time Series Analysis’, pp. 34–6.Google Scholar

¹⁰ Miller, and Mackie, , ‘The Electoral Cycle’, p. 274.Google Scholar

¹¹ Goodhart, and Bhansali, , ‘Political Economy’, p. 92.Google Scholar

¹² The parameters are estimated from the observations expressed in deviations from the mean. In this case the constant term is zero when the series is stationary, and hence is omitted from the models in Table 4.

¹³ This was inferred from the residuals of the forecasting model. See Table 6, p. 231.

¹⁴ See Freund, J. E., Mathematical Statistics (London: Prentice-Hall International, 1972), pp. 220–3.Google Scholar

¹⁵ Goodhart, and Bhansali, , ‘Political Economy’, pp. 94–106Google Scholar. Spectral analysis involves decomposing the series into basic frequencies. If the series is stationary it can be decomposed into a set of uncorrelated components, each of which is related to a particular frequency in the data. It is then possible to identify the contribution of each frequency to the total variation in the series. The procedure is analogous to the analysis of variance. The periodicity of significant cycles can be identified using this technique. See Kendall, M. G., Time Series (London: C. Griffin, 1973), Chap. 8.Google Scholar

¹⁶ Goodhart, and Bhansali, , ‘Political Economy’, p. 97.Google Scholar

¹⁷ See Kendall, M. G. and Stuart, A., ‘The Law of Cubic Proportions in Electoral Results’, British Journal of Sociology, I (1950), 183–97CrossRefGoogle Scholar; March, J. G., ‘Party Legislative Representation as a Function of Election Results’, Public Opinion Quarterly, XI (1957), 521–42CrossRefGoogle Scholar; Qualter, T., ‘Seats and Votes: An Application of the Cube Law to the Canadian Electoral System’, Canadian Journal of Political Science, I (1968), 336–44CrossRefGoogle Scholar; and Tufte, E. R., ‘The Relationship between Seats and Votes in Two-party Systems’, American Political Science Review, LXVII (1973), 540–54.CrossRefGoogle Scholar

¹⁸ Kendall, and Stuart, , ‘The Law of Cubic Proportions’, p. 190.Google Scholar

¹⁹ Laakso, Markku, ‘Should a Two-and-a-Half Law replace the Cube Law in British Elections?’, British Journal of Political Science (forthcoming).Google Scholar

²⁰ In the Hamilton by-election on the 31 May 1978 there was a 2·5 per cent swing to Labour from the Scottish National party. The Gallup poll for Great Britain taken on the 18 May 1978 showed Labour and the Conservatives to be neck-and-neck in the polls, each with a support of 43·5 per cent. This contrasted sharply with the position in May 1977 when the Conservatives had a 20·5 per cent lead over Labour. See The Gallup Political Index, Report No. 214 (London: Gallup Polls Ltd., 1978), Table 1.Google Scholar