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 134.03% per annum.
- AAL price at the close of February 21, 2024 was $14.79 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 28.90% per annum.
- AAL price at the close of February 21, 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 AAL 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: October 13, 2023
End date: February 21, 2024
a = -1.5191
b = 0.0023
s = 0.0444
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0023) – 1
= 134.03%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0444) – 1
= 19.42%
October 13, 2023 calculations
Top border of price channel:
Exp(Y1,169)
= Exp(a + b × X1,169 + 2 × s)
= Exp(a + b × 1,694 + 2 × s)
= Exp(-1.5191 + 0.0023 × 1,694 + 2 × 0.0444)
= Exp(2.5159)
= $12.38
Bottom border of price channel:
Exp(Y1,169)
= Exp(a + b × X1,169 – 2 × s)
= Exp(a + b × 1,694 – 2 × s)
= Exp(-1.5191 + 0.0023 × 1,694 – 2 × 0.0444)
= Exp(2.3384)
= $10.36
February 21, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(-1.5191 + 0.0023 × 1,825 + 2 × 0.0444)
= Exp(2.8210)
= $16.79
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(-1.5191 + 0.0023 × 1,825 – 2 × 0.0444)
= Exp(2.6436)
= $14.06
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 134.03% per annum.
- AAL price at the close of February 21, 2024 was $14.79 and was inside the primary price channel.
Secondary Trend
Start date: February 6, 2024
End date: February 21, 2024
a = 4.3939
b = -0.0009
s = 0.0071
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0009) – 1
= -28.90%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0071) – 1
= 2.87%
February 6, 2024 calculations
Top border of price channel:
Exp(Y1,247)
= Exp(a + b × X1,247 + 2 × s)
= Exp(a + b × 1,810 + 2 × s)
= Exp(4.3939 + -0.0009 × 1,810 + 2 × 0.0071)
= Exp(2.7168)
= $15.13
Bottom border of price channel:
Exp(Y1,247)
= Exp(a + b × X1,247 – 2 × s)
= Exp(a + b × 1,810 – 2 × s)
= Exp(4.3939 + -0.0009 × 1,810 – 2 × 0.0071)
= Exp(2.6885)
= $14.71
February 21, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(4.3939 + -0.0009 × 1,825 + 2 × 0.0071)
= Exp(2.7028)
= $14.92
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(4.3939 + -0.0009 × 1,825 – 2 × 0.0071)
= Exp(2.6745)
= $14.50
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 28.90% per annum.
- AAL price at the close of February 21, 2024 was inside the secondary price channel.
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