R Notebook

sample size

library(gtsummary)
library(dplyr)

Major European Stock Indices, 1991–1998

EuStockMarkets

Time Series:
Start = c(1991, 130) 
End = c(1998, 169) 
Frequency = 260 
             DAX    SMI    CAC   FTSE
1991.496 1628.75 1678.1 1772.8 2443.6
1991.500 1613.63 1688.5 1750.5 2460.2
1991.504 1606.51 1678.6 1718.0 2448.2
1991.508 1621.04 1684.1 1708.1 2470.4
1991.512 1618.16 1686.6 1723.1 2484.7
1991.515 1610.61 1671.6 1714.3 2466.8
1991.519 1630.75 1682.9 1734.5 2487.9
1991.523 1640.17 1703.6 1757.4 2508.4
1991.527 1635.47 1697.5 1754.0 2510.5
1991.531 1645.89 1716.3 1754.3 2497.4
1991.535 1647.84 1723.8 1759.8 2532.5
1991.538 1638.35 1730.5 1755.5 2556.8
1991.542 1629.93 1727.4 1758.1 2561.0
1991.546 1621.49 1733.3 1757.5 2547.3
1991.550 1624.74 1734.0 1763.5 2541.5
1991.554 1627.63 1728.3 1762.8 2558.5
1991.558 1631.99 1737.1 1768.9 2587.9
1991.562 1621.18 1723.1 1778.1 2580.5
1991.565 1613.42 1723.6 1780.1 2579.6
1991.569 1604.95 1719.0 1767.7 2589.3
1991.573 1605.75 1721.2 1757.9 2595.0
1991.577 1616.67 1725.3 1756.6 2595.6
1991.581 1619.29 1727.2 1754.7 2588.8
1991.585 1620.49 1727.2 1766.8 2591.7
1991.588 1619.67 1731.6 1766.5 2601.7
1991.592 1623.07 1724.1 1762.2 2585.4
1991.596 1613.98 1716.9 1759.5 2573.3
1991.600 1631.87 1723.4 1782.4 2597.4
1991.604 1630.37 1723.0 1789.5 2600.6
1991.608 1633.47 1728.4 1783.5 2570.6
1991.612 1626.55 1722.1 1780.4 2569.4
1991.615 1650.43 1724.5 1808.8 2584.9
1991.619 1650.06 1733.6 1820.3 2608.8
1991.623 1654.11 1739.0 1820.3 2617.2
1991.627 1653.60 1726.2 1820.3 2621.0
1991.631 1501.82 1587.4 1687.5 2540.5
1991.635 1524.28 1630.6 1725.6 2554.5
1991.638 1603.65 1685.5 1792.9 2601.9
1991.642 1622.49 1701.3 1819.1 2623.0
1991.646 1636.68 1718.0 1833.5 2640.7
1991.650 1652.10 1726.2 1853.4 2640.7
1991.654 1645.81 1716.6 1849.7 2619.8
1991.658 1650.36 1725.8 1851.8 2624.2
1991.662 1651.55 1737.4 1857.7 2638.2
1991.665 1649.88 1736.6 1864.3 2645.7
1991.669 1653.52 1732.4 1863.5 2679.6
1991.673 1657.51 1731.2 1873.2 2669.0
1991.677 1649.55 1726.9 1860.8 2664.6
1991.681 1649.09 1727.8 1868.7 2663.3
1991.685 1646.41 1720.2 1860.4 2667.4
1991.688 1638.65 1715.4 1855.9 2653.2
1991.692 1625.80 1708.7 1840.5 2630.8
1991.696 1628.64 1713.0 1842.6 2626.6
1991.700 1632.22 1713.5 1861.2 2641.9
1991.704 1633.65 1718.0 1876.2 2625.8
1991.708 1631.17 1701.7 1878.3 2606.0
1991.712 1635.80 1701.7 1878.4 2594.4
1991.715 1621.27 1684.9 1869.4 2583.6
1991.719 1624.70 1687.2 1880.4 2588.7
1991.723 1616.13 1690.6 1885.5 2600.3
1991.727 1618.12 1684.3 1888.4 2579.5
1991.731 1627.80 1679.9 1885.2 2576.6
1991.735 1625.79 1672.9 1877.9 2597.8
1991.738 1614.80 1663.1 1876.5 2595.6
1991.742 1612.80 1669.3 1883.8 2599.0
1991.746 1605.47 1664.7 1880.6 2621.7
1991.750 1609.32 1672.3 1887.4 2645.6
1991.754 1607.48 1687.7 1878.3 2644.2
1991.758 1607.48 1686.8 1867.1 2625.6
1991.762 1604.89 1686.6 1851.9 2624.6
1991.765 1589.12 1675.8 1843.6 2596.2
1991.769 1582.27 1677.4 1848.1 2599.5
1991.773 1567.99 1673.2 1843.4 2584.1
1991.777 1568.16 1665.0 1843.6 2570.8
1991.781 1569.71 1671.3 1833.8 2555.0
1991.785 1571.74 1672.4 1833.4 2574.5
1991.788 1585.41 1676.2 1856.9 2576.7
1991.792 1570.01 1692.6 1863.4 2579.0
1991.796 1561.89 1696.5 1855.5 2588.7
1991.800 1565.18 1716.1 1864.2 2601.1
1991.804 1570.34 1713.3 1846.0 2575.7
1991.808 1577.00 1705.1 1836.8 2559.5
1991.812 1590.29 1711.3 1830.4 2561.1
1991.815 1572.72 1709.8 1831.6 2528.3
1991.819 1572.07 1688.6 1834.8 2514.7
1991.823 1579.19 1698.9 1852.1 2558.5
1991.827 1588.73 1700.0 1849.8 2553.3
1991.831 1586.01 1693.0 1861.8 2577.1
1991.835 1579.77 1683.9 1856.7 2566.0
1991.838 1572.58 1679.2 1856.7 2549.5
1991.842 1568.09 1673.9 1841.5 2527.8
1991.846 1578.21 1683.9 1846.9 2540.9
1991.850 1573.94 1688.4 1836.1 2534.2
1991.854 1582.06 1693.9 1838.6 2538.0
1991.858 1610.18 1720.9 1857.6 2559.0
1991.862 1605.16 1717.9 1857.6 2554.9
1991.865 1623.84 1733.6 1858.4 2575.5
1991.869 1615.26 1729.7 1846.8 2546.5
1991.873 1627.08 1735.6 1868.5 2561.6
1991.877 1626.97 1734.1 1863.2 2546.6
1991.881 1605.70 1699.3 1808.3 2502.9
1991.885 1589.70 1678.6 1765.1 2463.1
1991.888 1589.70 1675.5 1763.5 2472.6
1991.892 1603.26 1670.1 1766.0 2463.5
1991.896 1599.75 1652.2 1741.3 2446.3
1991.900 1590.86 1635.0 1743.3 2456.2
1991.904 1603.50 1654.9 1769.0 2471.5
1991.908 1589.86 1642.0 1757.9 2447.5
1991.912 1587.92 1638.7 1754.9 2428.6
1991.915 1571.06 1622.6 1739.7 2420.2
1991.919 1549.81 1596.1 1708.8 2414.9
1991.923 1549.36 1612.4 1722.2 2420.2
1991.927 1554.65 1625.0 1713.9 2423.8
1991.931 1557.52 1610.5 1703.2 2407.0
1991.935 1555.31 1606.6 1685.7 2388.7
1991.938 1559.76 1610.7 1663.4 2409.6
1991.942 1548.44 1603.1 1636.9 2392.0
1991.946 1543.99 1591.5 1645.6 2380.2
1991.950 1550.21 1605.2 1671.6 2423.3
1991.954 1557.03 1621.4 1688.3 2451.6
1991.958 1551.78 1622.5 1696.8 2440.8
1991.962 1562.89 1626.6 1711.7 2432.9
1991.965 1570.28 1627.4 1706.2 2413.6
1991.969 1559.26 1614.9 1684.2 2391.6
1991.973 1545.87 1602.3 1648.5 2358.1
1991.977 1542.77 1598.3 1633.6 2345.4
1991.981 1542.77 1627.0 1699.1 2384.4
1991.985 1542.77 1627.0 1699.1 2384.4
1991.988 1542.77 1627.0 1722.5 2384.4
1991.992 1564.27 1655.7 1720.7 2418.7
1991.996 1577.26 1670.1 1741.9 2420.0
1992.000 1577.26 1670.1 1765.7 2493.1
1992.004 1577.26 1670.1 1765.7 2493.1
1992.008 1598.19 1670.1 1749.9 2492.8
1992.012 1604.05 1704.0 1770.3 2504.1
1992.015 1604.69 1711.8 1787.6 2493.2
1992.019 1593.65 1700.5 1778.7 2482.9
1992.023 1581.68 1690.3 1785.6 2467.1
1992.027 1599.14 1715.4 1833.9 2497.9
1992.031 1613.82 1723.5 1837.4 2477.9
1992.035 1620.45 1719.4 1824.3 2490.1
1992.038 1629.51 1734.4 1843.8 2516.3
1992.042 1663.70 1772.8 1873.6 2537.1
1992.046 1664.09 1760.3 1860.2 2541.6
1992.050 1669.29 1747.2 1860.2 2536.7
1992.054 1685.14 1750.2 1865.9 2544.9
1992.058 1687.07 1755.3 1867.9 2543.4
1992.062 1680.13 1754.6 1841.3 2522.0
1992.065 1671.84 1751.2 1838.7 2525.3
1992.069 1669.52 1752.5 1849.9 2510.4
1992.073 1686.71 1769.4 1869.3 2539.9
1992.077 1685.51 1767.6 1890.6 2552.0
1992.081 1671.01 1750.0 1879.6 2546.5
1992.085 1683.06 1747.1 1873.9 2550.8
1992.088 1685.70 1753.5 1875.3 2571.2
1992.092 1685.66 1752.8 1857.0 2560.2
1992.096 1678.77 1752.9 1856.5 2556.8
1992.100 1685.85 1764.7 1865.8 2547.1
1992.104 1683.71 1776.8 1860.6 2534.3
1992.108 1686.59 1779.3 1861.6 2517.2
1992.112 1683.73 1785.1 1865.6 2538.4
1992.115 1679.14 1798.2 1864.1 2537.1
1992.119 1685.03 1794.1 1861.6 2523.7
1992.123 1680.81 1795.2 1876.5 2522.6
1992.127 1676.17 1780.4 1865.1 2513.9
1992.131 1688.46 1789.5 1882.1 2541.0
1992.135 1696.55 1794.2 1912.2 2555.9
1992.138 1690.24 1784.4 1915.4 2536.7
1992.142 1711.35 1800.1 1951.2 2543.4
1992.146 1711.29 1804.0 1962.4 2542.3
1992.150 1729.86 1816.2 1976.5 2559.7
1992.154 1716.63 1810.5 1953.5 2546.8
1992.158 1743.36 1821.9 1981.3 2565.0
1992.162 1745.17 1828.2 1985.1 2562.0
1992.165 1746.76 1840.6 1983.4 2562.1
1992.169 1749.29 1841.1 1979.7 2554.3
1992.173 1763.86 1846.3 1983.8 2565.4
1992.177 1762.27 1850.0 1988.1 2558.4
1992.181 1762.29 1839.0 1973.0 2538.3
1992.185 1746.77 1820.2 1966.9 2533.1
1992.188 1753.50 1815.2 1976.3 2550.7
1992.192 1753.21 1820.6 1993.9 2574.8
1992.196 1739.88 1807.1 1968.0 2522.4
1992.200 1723.92 1791.4 1941.8 2493.3
1992.204 1734.42 1806.2 1947.1 2476.0
1992.208 1723.13 1798.7 1929.2 2470.7
1992.212 1732.92 1818.2 1943.6 2491.2
1992.215 1729.89 1820.5 1928.2 2464.7
1992.219 1725.74 1833.3 1922.0 2467.6
1992.223 1730.90 1837.1 1919.1 2456.6
1992.227 1714.17 1818.2 1884.6 2441.0
1992.231 1716.20 1824.1 1896.3 2458.7
1992.235 1719.06 1830.1 1928.3 2464.9
1992.238 1718.21 1835.6 1934.8 2472.2
1992.242 1698.84 1828.7 1923.5 2447.9
1992.246 1714.76 1839.2 1943.8 2452.9
1992.250 1718.35 1837.2 1942.4 2440.1
1992.254 1706.69 1826.7 1928.1 2408.6
1992.258 1723.37 1838.0 1942.0 2405.4
1992.262 1716.18 1829.1 1942.7 2382.7
1992.265 1738.78 1843.1 1974.8 2400.9
1992.269 1737.41 1850.5 1975.4 2404.2
1992.273 1714.77 1827.1 1907.5 2393.2
1992.277 1724.24 1829.1 1943.6 2436.4
1992.281 1733.77 1848.0 1974.1 2572.6
1992.285 1729.96 1840.5 1963.3 2591.0
1992.288 1734.46 1853.8 1972.3 2600.5
1992.292 1744.35 1874.1 1990.7 2640.2
1992.296 1746.88 1871.3 1978.2 2638.6
1992.300 1746.88 1871.3 1978.2 2638.6
1992.304 1746.88 1871.3 1978.2 2638.6
1992.308 1747.47 1860.5 1980.4 2625.8
1992.312 1753.10 1874.7 1983.7 2607.8
1992.315 1745.17 1880.1 1978.1 2609.8
1992.319 1745.72 1874.7 1984.9 2643.0
1992.323 1742.92 1875.6 1995.7 2658.2
1992.327 1731.68 1859.5 2006.6 2651.0
1992.331 1731.18 1874.2 2036.7 2664.9
1992.335 1728.09 1880.1 2031.1 2654.1
1992.338 1728.09 1880.1 2031.1 2659.8
1992.342 1731.29 1907.7 2041.6 2659.8
1992.346 1733.82 1920.5 2046.9 2662.2
1992.350 1745.78 1937.3 2047.2 2698.7
1992.354 1752.57 1936.8 2063.4 2701.9
1992.358 1748.13 1949.1 2063.4 2725.7
1992.362 1750.70 1963.7 2077.5 2737.8
1992.365 1747.91 1950.8 2063.6 2722.4
1992.369 1745.79 1953.5 2053.2 2720.5
1992.373 1735.34 1945.0 2017.0 2694.7
1992.377 1719.92 1921.1 2024.0 2682.6
1992.381 1763.59 1939.1 2051.6 2703.6
1992.385 1766.76 1928.0 2023.1 2700.6
1992.388 1785.40 1933.4 2030.8 2711.9
1992.392 1783.56 1925.7 2016.8 2702.0
1992.396 1804.42 1931.7 2045.1 2715.0
1992.400 1812.33 1928.7 2046.3 2715.0
1992.404 1799.51 1924.5 2029.6 2704.6
1992.408 1792.80 1914.2 2014.1 2698.6
1992.412 1792.80 1914.2 2014.1 2694.2
1992.415 1806.36 1920.6 2033.3 2707.6
1992.419 1798.23 1923.3 2017.4 2697.6
1992.423 1800.62 1930.4 2024.9 2705.9
1992.427 1786.19 1915.2 1992.6 2680.9
1992.431 1791.35 1916.9 1994.9 2681.9
1992.435 1789.05 1913.8 1981.6 2668.5
1992.438 1789.05 1913.8 1981.6 2645.8
1992.442 1784.71 1899.7 1962.2 2635.4
1992.446 1789.45 1888.0 1953.7 2636.1
1992.450 1779.74 1868.8 1928.8 2614.1
1992.454 1786.97 1879.9 1928.3 2603.7
 [ reached 'max' / getOption("max.print") -- omitted 1610 rows ]

data(EuStockMarkets)
summary(EuStockMarkets)

      DAX            SMI            CAC            FTSE     
 Min.   :1402   Min.   :1587   Min.   :1611   Min.   :2281  
 1st Qu.:1744   1st Qu.:2166   1st Qu.:1875   1st Qu.:2843  
 Median :2141   Median :2796   Median :1992   Median :3247  
 Mean   :2531   Mean   :3376   Mean   :2228   Mean   :3566  
 3rd Qu.:2722   3rd Qu.:3812   3rd Qu.:2274   3rd Qu.:3994  
 Max.   :6186   Max.   :8412   Max.   :4388   Max.   :6179  

head(EuStockMarkets)

Time Series:
Start = c(1991, 130) 
End = c(1991, 135) 
Frequency = 260 
             DAX    SMI    CAC   FTSE
1991.496 1628.75 1678.1 1772.8 2443.6
1991.500 1613.63 1688.5 1750.5 2460.2
1991.504 1606.51 1678.6 1718.0 2448.2
1991.508 1621.04 1684.1 1708.1 2470.4
1991.512 1618.16 1686.6 1723.1 2484.7
1991.515 1610.61 1671.6 1714.3 2466.8

DAX: German stock index (Ibis) SMI: Swiss Market Index CAC: French CAC 40 index FTSE: UK FTSE 100 index

class(EuStockMarkets)

[1] "mts"    "ts"     "matrix" "array" 

str(EuStockMarkets)

 Time-Series [1:1860, 1:4] from 1991 to 1999: 1629 1614 1607 1621 1618 ...
 - attr(*, "dimnames")=List of 2
  ..$ : NULL
  ..$ : chr [1:4] "DAX" "SMI" "CAC" "FTSE"

components.ts = decompose(ftse)
plot(components.ts)

Interpretation:

Dataset Overview

EuStockMarkets is a built-in R dataset containing daily closing prices of four major European stock indices from 1991 to 1998:

DAX – Germany

SMI – Switzerland

CAC – France

FTSE – UK

It’s a ts (time series) object.

2. summary(EuStockMarkets)

This gives the minimum, median, mean, and maximum values for each index.

You’ll see that the DAX and SMI are generally higher on average than CAC and FTSE.

The range tells you about volatility: wider ranges suggest more variation in stock index levels.

3. head(EuStockMarkets)

This shows the first few rows (early 1991 values).

Useful to see how the data begins and confirm the structure.

For example, you might notice that all indices start at different base levels.

4. class(EuStockMarkets)

The output should be “mts” “ts”.

“ts” = time series object.

“mts” = multiple time series (since we have four indices recorded simultaneously).

5. str(EuStockMarkets)

This displays the structure:

Time series length (~1860 observations).

Frequency = 260 (roughly trading days per year).

Start year = 1991, end = 1998.

Each column is one stock index.

6. components.ts = decompose(ftse)

Here’s the tricky part:

ftse must first be extracted, e.g.

ftse <- EuStockMarkets[,“FTSE”]

decompose() works only on a univariate time series with a clear seasonal component.

👉 But: Stock data usually doesn’t have strong seasonality, so decompose() isn’t always meaningful. Still, if you run it, you’ll get:

Trend: The long-term movement of FTSE (upward or downward over the years).

Seasonal: Regular repeating patterns within each year (but here it may be flat or noisy, since stock markets don’t follow strict seasonality like sales data).

Random (remainder): Residual fluctuations not explained by trend or seasonality → this will be large for financial data.

7. plot(components.ts)

The plot shows:

Observed (original FTSE values).

Trend (smoothed curve showing general direction, e.g., upward trend in the 1990s).

Seasonal (should be near zero or flat, since stocks don’t have strong seasonality).

Random (irregular ups and downs = market volatility).

✅ Interpretation:

The trend will likely show FTSE steadily rising from 1991 to the mid/late 1990s.

The seasonal component won’t be significant (stocks are influenced by macroeconomic/political events, not yearly cycles).

The random component dominates, reflecting the unpredictability of stock market movements.