Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 26.59% per annum.
- TGT price at the close of April 24, 2024 was $165.34 and was higher than the top border of the primary price channel by $35.67 (27.51%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 144.55% per annum.
- TGT price at the close of April 24, 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 TGT 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 29, 2021
End date: December 12, 2023
a = 6.1985
b = -0.0008
s = 0.1063
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0008) – 1
= -26.59%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1063) – 1
= 52.98%
April 29, 2021 calculations
Top border of price channel:
Exp(Y507)
= Exp(a + b × X507 + 2 × s)
= Exp(a + b × 735 + 2 × s)
= Exp(6.1985 + -0.0008 × 735 + 2 × 0.1063)
= Exp(5.7887)
= $326.59
Bottom border of price channel:
Exp(Y507)
= Exp(a + b × X507 – 2 × s)
= Exp(a + b × 735 – 2 × s)
= Exp(6.1985 + -0.0008 × 735 – 2 × 0.1063)
= Exp(5.3636)
= $213.49
December 12, 2023 calculations
Top border of price channel:
Exp(Y1,167)
= Exp(a + b × X1,167 + 2 × s)
= Exp(a + b × 1,692 + 2 × s)
= Exp(6.1985 + -0.0008 × 1,692 + 2 × 0.1063)
= Exp(4.9784)
= $145.25
Bottom border of price channel:
Exp(Y1,167)
= Exp(a + b × X1,167 – 2 × s)
= Exp(a + b × 1,692 – 2 × s)
= Exp(6.1985 + -0.0008 × 1,692 – 2 × 0.1063)
= Exp(4.5533)
= $94.95
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 26.59% per annum.
- TGT price at the close of April 24, 2024 was $165.34 and was higher than the top border of the primary price channel by $35.67 (27.51%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: September 22, 2023
End date: April 23, 2024
a = 0.7176
b = 0.0025
s = 0.0469
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0025) – 1
= 144.55%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0469) – 1
= 20.62%
September 22, 2023 calculations
Top border of price channel:
Exp(Y1,111)
= Exp(a + b × X1,111 + 2 × s)
= Exp(a + b × 1,611 + 2 × s)
= Exp(0.7176 + 0.0025 × 1,611 + 2 × 0.0469)
= Exp(4.7583)
= $116.55
Bottom border of price channel:
Exp(Y1,111)
= Exp(a + b × X1,111 – 2 × s)
= Exp(a + b × 1,611 – 2 × s)
= Exp(0.7176 + 0.0025 × 1,611 – 2 × 0.0469)
= Exp(4.5708)
= $96.62
April 23, 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(0.7176 + 0.0025 × 1,825 + 2 × 0.0469)
= Exp(5.2826)
= $196.89
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(0.7176 + 0.0025 × 1,825 – 2 × 0.0469)
= Exp(5.0951)
= $163.23
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 144.55% per annum.
- TGT price at the close of April 24, 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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