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 129.84% per annum.
- TGT price at the close of March 25, 2025 was $105.40 and was lower than the bottom border of the primary price channel by $4,635.30 (97.78%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 12.76% per annum.
- TGT price at the close of March 25, 2025 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 5, 2021
End date: August 16, 2021
a = 4.3380
b = 0.0023
s = 0.0176
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0023) – 1
= 129.84%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0176) – 1
= 7.29%
April 5, 2021 calculations
Top border of price channel:
Exp(Y257)
= Exp(a + b × X257 + 2 × s)
= Exp(a + b × 375 + 2 × s)
= Exp(4.3380 + 0.0023 × 375 + 2 × 0.0176)
= Exp(5.2282)
= $186.46
Bottom border of price channel:
Exp(Y257)
= Exp(a + b × X257 – 2 × s)
= Exp(a + b × 375 – 2 × s)
= Exp(4.3380 + 0.0023 × 375 – 2 × 0.0176)
= Exp(5.1578)
= $173.78
August 16, 2021 calculations
Top border of price channel:
Exp(Y350)
= Exp(a + b × X350 + 2 × s)
= Exp(a + b × 508 + 2 × s)
= Exp(4.3380 + 0.0023 × 508 + 2 × 0.0176)
= Exp(5.5315)
= $252.51
Bottom border of price channel:
Exp(Y350)
= Exp(a + b × X350 – 2 × s)
= Exp(a + b × 508 – 2 × s)
= Exp(4.3380 + 0.0023 × 508 – 2 × 0.0176)
= Exp(5.4611)
= $235.35
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 129.84% per annum.
- TGT price at the close of March 25, 2025 was $105.40 and was lower than the bottom border of the primary price channel by $4,635.30 (97.78%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: April 5, 2021
End date: March 25, 2025
a = 5.4625
b = -0.0004
s = 0.1486
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0004) – 1
= -12.76%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1486) – 1
= 81.19%
April 5, 2021 calculations
Top border of price channel:
Exp(Y257)
= Exp(a + b × X257 + 2 × s)
= Exp(a + b × 375 + 2 × s)
= Exp(5.4625 + -0.0004 × 375 + 2 × 0.1486)
= Exp(5.6194)
= $275.73
Bottom border of price channel:
Exp(Y257)
= Exp(a + b × X257 – 2 × s)
= Exp(a + b × 375 – 2 × s)
= Exp(5.4625 + -0.0004 × 375 – 2 × 0.1486)
= Exp(5.0251)
= $152.18
March 25, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(5.4625 + -0.0004 × 1,825 + 2 × 0.1486)
= Exp(5.0773)
= $160.34
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(5.4625 + -0.0004 × 1,825 – 2 × 0.1486)
= Exp(4.4829)
= $88.49
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 12.76% per annum.
- TGT price at the close of March 25, 2025 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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