6: Prices Dynamics Over Time
- Page ID
- 299290
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The overall aim of this chapter to provide you with some basic tools to work with and make sense of information contained in a price series. The specific objectives of this chapter are as follows:
- Explain the four components of a price series.
- Use index numbers to account for inflation and express monetary values in constant dollars.
- Compute an N-period moving average to remove the seasonal component from a price series.
- Distinguish between demand and supply induced seasonality and be able to provide examples of each.
- Describe conditions that are likely to give rise to price cycles.
Markets can be defined in terms of three dimensions (1) a product or service, (2) a location, and (3) a point in time. This chapter emphasizes prices over time. What constitutes a point in time can vary depending on the question being asked and the product and geographic context of the market. In markets for commodity futures and options, high-frequency intraday prices are available, but it has also been common to analyze daily reference points such as the open, close or settlement price. Cash prices for some agricultural commodities are reported daily or weekly. Monthly or quarterly periodicities are also common. In this chapter, you will learn to think about price series in terms of several components. A time series can be decomposed into four components as illustrated in quarterly price series presented in Demonstration 1. Specifically, these components are:
- The trend. The trend is the general long-term direction of movement in the series. Demonstration 1 shows a positive trend, with prices increasing with time. To better visualize the trend in Demonstration 1, remove every other component but the trend from the demonstration.
- The seasonal component. A seasonal pattern is observed with regularity over a year. Use Demonstration 1 to remove everything but the seasonal component. Look at the series carefully and you will see that the price is highest in the first quarter of the year and is lowest in the third quarter. This pattern repeats itself each year.
- The cyclical component. A cyclical pattern repeats with some regularity over several years. Cyclical patterns differ from seasonal patterns in that cyclical patterns occur over multiple years, whereas seasonal patterns occur within one year. In Demonstration 1, remove all components but the cyclical component. The period shown illustrates one full cycle from a peak in quarter 1 to another peak in quarter 22. Thus, the cycle shown lasts about 5.5 years.
- The random component. Movements in the series that cannot be explained by the trend, seasonal, or cyclical components are considered to be random.
Demonstration 1. The Components of a Time Series
- 6.1: The Trend
- This page explores price trends, emphasizing the distinction between nominal and real prices influenced by supply and demand. It discusses regression analysis to identify long-term trends while filtering out seasonal fluctuations, and the significance of using real prices for accurate evaluations impacted by inflation.
- 6.2: Seasonal Component
- This page discusses seasonal patterns that influence demand and supply throughout the year, highlighting demand spikes during holidays and supply fluctuations for perishable goods. It notes the role of storage costs in pricing storable crops and emphasizes the use of moving averages to identify trends by filtering out seasonal effects, with the appropriate length of the average depending on the data frequency.
- 6.3: Cyclical Component
- This page discusses the differences between cyclical and seasonal patterns, highlighting the business cycle of economic expansions and recessions. It explains agricultural price cycles, particularly in livestock markets, influenced by producers' responses to price changes, with the cattle cycle lasting about 8 to 12 years.
- 6.4: Random Component
- This page explores random movements in time series data beyond trend, seasonal, or cyclical influences, pointing out external factors such as weather and political changes that affect supply and demand. It recommends using moving averages to filter out randomness and seasonal effects, while also noting that significant random shocks can disrupt cyclical price patterns, complicating empirical analysis.
- 6.5: Concluding Comments
- This page provides a concise overview of analyzing agricultural price time series data, outlining key components, inflation adjustment, and factors behind seasonal and cyclical patterns. It serves as an introduction suitable for general survey courses, with a recommendation to engage in problem sets for reinforcing the concepts.
- 6.6: References
- This page provides fundamental tools for analyzing agricultural price time series data, emphasizing the limitations of general surveys versus specialized programs. It covers identifying time series components, adjusting for inflation, and recognizing seasonal and cyclical patterns in commodity prices, with problem sets to enhance understanding.
- 6.7: Problem Sets
- This page includes exercises on inflation adjustment, converting nominal prices to constant dollars, and assessing understanding through multiple-choice questions on inflation and price indices. It also covers economic concepts of demand and supply influenced by seasonal patterns, highlighting scenarios affecting trends and methods for adjusting seasonal components in time series data.