# Glossary

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Amplitude | The degree of variation of any variable from its mean to its extremes. The range is twice the amplitude. |

Amplitude modulation | Cyclical Variations of the amplitude of a cyclical wave. See also Frequncy modulation. |

Aphelion | The direction of the furtherest point in a planets orbit from the Sun. |

Ascending node | The direction in a planets orbit when it crosses from south to north as it passes through the ecliptic. |

Conjunction | When two celestial bodies are at the same longitude. |

Correlation | The degree to which two variables move together, where 0 means there is no relationship, 1 means there is common movement and -1 means there is opposite movement. |

Cycle | A repetition of some conditions at a fairly regular time interval, known as the period of the cycle. Often data will have multiple cycles present, so only some aspect of the cycle repeats after the time interval. |

Cycle analysis | Finding periodic patterns in time series data, commonly by such tools as FFT or MESA. |

Descending node | The direction in a planets orbit when it crosses from north to south as it passes through the ecliptic. |

Ecliptic | The path of the Sun through the stars as seen from the earth. |

Exponential moving average. | A moving average with variable weights, more prominence being given to the later terms, and generally plotted at the last time point. Each term may be calculated by taking the last value by a constant plus the previous moving average times (1 – the same constant). |

FFT | An abbreviation for Fast Fourier Transform, a method of quickly analysing cycle frequencies on a computer, usually with data series that are a power of 2 long. |

Fourier analysis | A method of finding he frequencies (or periods) present in a time series by decomposing it in to a series of sine waves as demonstrated by the mathematician Fourier. |

Frequency | The number of cycles occuring per unit of time. The units are 1/time. Freqency is the inverse of period. |

Frequency modulation | Cyclical variations in the frequency of a cyclical wave. See also amplitude modulation. |

Fundamental | The lowest frequency, of which others are a multiple. When a time series is analysed by FFT, the length of time of the available data will be a fundamental for all the periods found. |

Harmonics | Are exact frequency multiples of any cycle (or exact period fractions). |

Idealized cycle | The average shape of a cycle plotted repeatedly and regularly through time for comparison to the actual data. |

Index | An average of multiple variables that is therefore indicative of a wider range of conditions and may be used for comparison. For example a stock market index is the average (usually weighted) of company stock prices. |

Indicators | Series derived from original data to highlight particular features of the data and give signals for traders to take action. An example is the difference between two moving averages, either simple or exponential. Over recent decades a large number of different indicators have been designed by traders. |

Interpolate | To fill in gaps in a time series by estimates when data is missing. |

Juglar cycle | A cycle of about 9 to 11 years named after Clement Juglar. He found boom and bust cycles in interest rates with repetition of the conditions of prosperity, crisis, liquidation and recession |

Kitchen cycle | A cycle of typically 39 to 41 months often reported in stocks and financial instruments and named after Joseph Kitchin. According to Edward R Dewey the average period is 40.68 months. |

Kondratieff cycle | A cycle usually reported as averaging 53 to 54 years named after Nikolai Kondratieff, a Russian researcher. Also called long wave and K-wave |

Kuznets cycle | A cycle of 16.5 to 18 years named after Simon Kuznets, a nobel prize-winner for his econometric work. |

Lag | To have variations later. Used particularly with variables such as economic activity. See also Lead. |

Lead | To have variations sooner. See also Lag. |

Log scale | In a graph, a log scale means that equal ratios are presented with equal spacing rather than equal differences. |

Mean | The average value of the data in a time series. |

MESA | An abbreviation for Maximum Entropy Spectral Analysis, a technique designed by Bourg for finding accurate frequencies for multiple cycles, even in short data series. |

Modulation | Cyclical variations in the frequency and / or amplitude of a cycle. |

Moving average | The average of a number of adjacent terms in a time series. They may be plotted at the center of the period (centred) or the end of the period (lagged). See also Exponential moving average. |

Opposition | When two celestial bodies are opposite in their orbits. |

Perihelion | The direction of a planet when it is at the nearest point to the Sun in its orbit. |

Period | The length of time between repetitions in a cycle. The units are time. Period is the inverse of frequency. Periodicity means exact regularity, something mot really found in nature. |

Phase | The timing of a cycle or wave as regards peaks and troughs in comparison to other cycles or waves of the same period. To be in phase is to have the same timing of peaks whereas to be out of phase has different timing. |

Resonance | The introduction of an oscillation in one system from a causally connected system that is oscillating at a frequency near to the / a natural frequency of that system. The nearer that the frequencies match and the less the natural losses of the resonating system are, the greater will be the induced resonance. |

Seasonal variation | Variation that follows the seasons and therefore has a fundamental cycle period of one year. A seasonal variation may have a shape different from a regular sine wave. |

Siderial year | The period, 365.25636 days when the earth comes back to the same point in its orbit relative to the stars. |

Siderial period | A period measured relative to the stars. |

Smoothing | The removal of the shorter term fluctuations in data. This is often done by a moving average of one sort or another. |

Spectrum | Originally the spread of light of different frequencies by a prism. Later, the same spread of frequencies by mathematical analysis of a time series, usually using Fourier Analysis especially FFT. |

Synodic period | The time that it takes one planet to overtake another in its orbit (on average). |

Time series | A set of measurements of something, usually at regular time intervals, in numerical form. |

Trend | The centre line running through data that is generally moving up or down over time. Mathematically it is established by the sum of least squares of the distances of the data points from the line. |

Tropical year | The year of the seasons, 365.24220 days, which is when the earth comes back to the same point in its orbit relative to its axial tilt. |

Varves | Geological layers deposited regularly, usually annually. |

Weighted | Combining in some proportions. A weighted moving average might for example multiply 5 successive values in a time series by 1, 2, 3, 2, 1 and add the results up and divide by 10. |