Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 54.65% per annum.
- BA price at the close of May 17, 2024 was $184.95 and was lower than the bottom border of the primary price channel by $87.58 (32.14%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 6.65% per annum.
- BA price at the close of May 17, 2024 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of BA price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: April 26, 2022
End date: September 7, 2023
a = 3.6088
b = 0.0012
s = 0.0899
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0012) – 1
= 54.65%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0899) – 1
= 43.28%
April 26, 2022 calculations
Top border of price channel:
Exp(Y740)
= Exp(a + b × X740 + 2 × s)
= Exp(a + b × 1,072 + 2 × s)
= Exp(3.6088 + 0.0012 × 1,072 + 2 × 0.0899)
= Exp(5.0691)
= $159.03
Bottom border of price channel:
Exp(Y740)
= Exp(a + b × X740 – 2 × s)
= Exp(a + b × 1,072 – 2 × s)
= Exp(3.6088 + 0.0012 × 1,072 – 2 × 0.0899)
= Exp(4.7095)
= $110.99
September 7, 2023 calculations
Top border of price channel:
Exp(Y1,083)
= Exp(a + b × X1,083 + 2 × s)
= Exp(a + b × 1,571 + 2 × s)
= Exp(3.6088 + 0.0012 × 1,571 + 2 × 0.0899)
= Exp(5.6651)
= $288.63
Bottom border of price channel:
Exp(Y1,083)
= Exp(a + b × X1,083 – 2 × s)
= Exp(a + b × 1,571 – 2 × s)
= Exp(3.6088 + 0.0012 × 1,571 – 2 × 0.0899)
= Exp(5.3055)
= $201.45
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 54.65% per annum.
- BA price at the close of May 17, 2024 was $184.95 and was lower than the bottom border of the primary price channel by $87.58 (32.14%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: January 3, 2023
End date: May 17, 2024
a = 5.6267
b = -0.0002
s = 0.0891
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -6.65%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0891) – 1
= 42.80%
January 3, 2023 calculations
Top border of price channel:
Exp(Y913)
= Exp(a + b × X913 + 2 × s)
= Exp(a + b × 1,324 + 2 × s)
= Exp(5.6267 + -0.0002 × 1,324 + 2 × 0.0891)
= Exp(5.5551)
= $258.54
Bottom border of price channel:
Exp(Y913)
= Exp(a + b × X913 – 2 × s)
= Exp(a + b × 1,324 – 2 × s)
= Exp(5.6267 + -0.0002 × 1,324 – 2 × 0.0891)
= Exp(5.1988)
= $181.05
May 17, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(5.6267 + -0.0002 × 1,824 + 2 × 0.0891)
= Exp(5.4607)
= $235.27
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(5.6267 + -0.0002 × 1,824 – 2 × 0.0891)
= Exp(5.1045)
= $164.76
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 6.65% per annum.
- BA price at the close of May 17, 2024 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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